How to calculate the integral of the sum of two kernel density functions in R?

I want to calculate the non-deterministic integral (0 to t) of the sum of two kernel density functions in R. Here is the code that I wrote:?


library(ks)?library(rgl)
? ? zz <- " longitude ? latitude ? ?depth ? time ? ?magnitude? ? 363.218744 ?52.38412991 3.04532258 ?9.241866766 0.838097648363.685488 ?53.85946071 0.25531946 ?0.578126952 0.854703175319.732091 ?32.23166292 4.2952681 ? 1.06539397 ?0.781598317315.812817 ?36.98421462 3.27938697 ?2.295483245 0.769473951119.498255 ?75.1280934 ?0.83253364 ?8.783517513 0.969860223138.588107 ?169.629965 ?1.89874255 ?9.745653758 0.972609198139.158872 ?169.6452912 3.67211991 ?15.03850063 0.881092856139.247168 ?169.3478202 2.85800531 ?15.26106239 0.80957094565.1234 147.3603323 2.84478705 ?16.82280753 0.8795771565.55518 ? ?147.0377814 2.69845292 ?20.23640417 0.90054614467.954278 ? 148.6017748 3.41456545 ?21.21715903 0.96836922766.968587 ? 146.3484298 2.33379707 ?22.02860946 0.726200657359.087074 ?42.8644051 ?2.85850316 ?23.70757068 0.861703105357.875617 ?40.08052697 2.90391604 ?23.84198256 0.828534981358.483231 ?41.26875168 1.98773836 ?26.06830006 0.885146048358.218523 ?40.27344373 0.61176635 ?28.24887694 0.86766276356.391874 ? 87.82219658 1.18588976 ?31.82632342 0.76775520656.355593 ? 87.68729915 1.37666954 ?33.07983844 0.73135585956.274533 ? 88.16157107 1.8140712 ? 33.21245517 0.70299329758.264625 ? 90.59810498 0.71927382 ?36.35112295 0.717745991296.051213 ?47.32622119 3.55526758 ?37.01360264 0.796795711296.428135 ?47.14235728 0.37586386 ?40.99409991 0.933842952296.483974 ?47.11833773 1.63577079 ?42.59987436 0.800643576149.978704 ?40.21568522 0.86039359 ?43.88742522 0.885870584152.913486 ?41.02065553 1.60530239 ?44.22730093 0.997865715148.90665 ? 41.08012738 3.93188008 ?45.45667836 0.894401708346.076543 ?139.8808064 1.85955423 ?46.43473917 0.861932746346.414328 ?139.4533544 1.11412982 ?47.08968108 0.769676426345.144434 ?138.4076443 1.90880173 ?47.41656879 0.921949668347.214491 ?139.3465751 2.37729226 ?48.71147851 0.966697704332.753563 ?192.22991 ? 2.28814891 ?50.57969649 0.957942288334.317276 ?189.9511419 3.86455092 ?50.68494991 0.879118237333.754131 ?189.9786093 2.97285931 ?51.75537529 0.896425643369.001883 ?49.03757175 3.850737 ? ?53.25133012 0.974504198373.451478 ?47.04323055 2.68174275 ?53.26729487 0.829954924371.270915 ?48.75191315 1.48038601 ?53.65752507 0.786928227100.980042 ?229.3257773 0.34910759 ?53.95915957 0.88956469185.373887 ?191.1246659 0.77164573 ?55.59813846 0.788626552186.209454 ?190.9779546 1.56667836 ?57.767241 ? 0.886608637185.124518 ?191.2527261 0.29458722 ?60.01364617 0.714260258185.914337 ?190.2745825 2.52740599 ?60.61554743 0.99838296967.896372 ? 155.4809072 0.28886827 ?61.31286449 0.762029245142.43641 ? 227.5860602 4.14452355 ?62.29628681 0.882209187141.364062 ?228.3322702 4.1635609 ? 63.89678201 0.804289098347.840723 ?114.6970218 0.56248091 ?63.95948138 0.91532112253.564593 ?174.113376 ?1.2621932 ? 64.24838467 0.708397989253.984435 ?174.5656449 1.51828163 ?65.07176672 0.720052528253.0236 ? ?173.9265349 1.23375198 ?65.94064053 0.978119242231.629097 ?211.4394495 1.30405063 ?66.38331454 0.726331528232.328374 ?210.8879029 2.03407748 ?66.68961587 0.799719569232.644377 ?211.2277656 0.97238417 ?68.10333701 0.857854269232.56663 ? 211.1678557 0.13184224 ?68.29747246 0.773992637112.295704 ?228.7487399 2.55766852 ?70.99561628 0.862869837113.023663 ?228.1650996 3.59402383 ?71.87466297 0.934260355112.538871 ?228.4575775 1.45766956 ?77.57275212 0.856564714113.814248 ?228.2794604 3.42350373 ?78.59894388 0.97958498183.44226 ? 9.61564954 ?3.18554848 ?79.43332479 0.744133594183.54304 ? 9.19009803 ?3.26511022 ?80.64811426 0.825029711183.268762 ?9.301064 ? ?2.44033259 ?85.7161253 ?0.784087865.369079 ? ?116.1726895 1.63053766 ?86.89113268 0.8794300954.970461 ? ?116.4974335 2.93526191 ?87.42088984 0.7109424576.345342 ? ?116.6858803 0.89072222 ?87.63073063 0.7191059515.492747 ? ?115.8670653 1.61844848 ?89.67642448 0.796864752343.385969 ?193.322461 ?2.62979605 ?89.94483446 0.729513559344.352781 ?193.5268701 4.29402892 ?90.4154695 ?0.751013388345.668421 ?193.0400517 3.1033618 ? 91.93169629 0.81134914344.640169 ?194.248506 ?1.57956728 ?92.33756179 0.711928487167.038399 ?5.96957805 ?3.55962707 ?94.67162694 0.912772286166.987777 ?6.09536737 ?3.45933516 ?96.09079729 0.892402408168.510068 ?6.14462771 ?3.46656886 ?96.53093276 0.752218258167.103837 ?6.28745699 ?3.55633497 ?97.11208455 0.718645583183.30843 ? 45.57593198 0.24446465 ?98.29165891 0.821997826183.036565 ?51.9529565 ?0.52456176 ?98.81054412 0.838918878183.144323 ?45.93514679 0.47791706 ?99.81095514 0.76080229338.977521 ?169.6576259 2.49761535 ?100.8103695 0.960864967338.821559 ?170.0718334 2.66390501 ?101.5614461 0.879382111337.682972 ?172.5078824 2.44075925 ?102.5406185 0.706904061339.414764 ?168.484822 ?3.07636237 ?102.5455371 0.969827931336.702388 ?194.6364837 3.67393227 ?103.0440893 0.835883835360.026772 ?184.3444998 3.62982366 ?103.3028211 0.717407853361.460234 ?184.3184775 0.96558388 ?103.369371 ?0.731880813247.557142 ?184.8726881 4.39064255 ?103.4793669 0.999527587249.630948 ?186.9021382 3.2051117 ? 104.2020101 0.959898221246.647174 ?185.7989473 1.89101073 ?104.2744971 0.884561739248.079025 ?184.8060252 3.64218348 ?106.7323829 0.708083345343.213475 ?214.4993165 0.45176581 ?107.1307404 0.796756791345.720762 ?213.6341763 1.63235709 ?108.0652973 0.83913287345.016305 ?212.8656785 1.28675708 ?108.2516714 0.72970517345.462936 ?213.150121 ?2.88754323 ?110.0171049 0.871296443186.053395 ?7.62715418 ?2.02691573 ?112.650555 ?0.797762528182.455458 ?4.26944797 ?2.45740267 ?114.2678386 0.835147701182.235994 ?4.39627706 ?0.26503411 ?114.7318806 0.873353139409.403475 ?82.39618618 0.06216757 ?115.4464072 0.722453292409.052314 ?82.35559269 0.16314584 ?115.5665069 0.717202801215.780351 ?0.08912318 ?1.39563448 ?116.2344263 0.790286931214.837434 ?1.45883443 ?0.97705113 ?117.218643 ?0.856516375461.589113 ?9.86224616 ?0.9972708 ? 117.971268 ?0.868564071459.202929 ?11.42966468 1.15177071 ?118.8073097 0.772466431459.088894 ?15.47868051 2.3559397 ? 121.4164909 0.973816049256.903777 ?87.43673381 2.04200349 ?121.5194263 0.947720281257.382498 ?86.97386698 3.79079014 ?121.6251341 0.833363765256.697794 ?87.54199636 2.55432997 ?121.6996209 0.994618769222.945818 ?200.9308941 2.84077044 ?121.7241906 0.873480268222.819858 ?201.6746837 2.29641155 ?122.7084014 0.770327049222.130409 ?201.4562846 1.27840311 ?123.3858524 0.943177133384.260699 ?147.0320964 2.79131573 ?123.5775361 0.835382249381.993241 ?146.3060028 1.35450405 ?124.1866165 0.774990751382.080971 ?147.3370846 3.71228941 ?125.0491715 0.98663126381.648904 ?146.8234101 1.83454687 ?125.0912787 0.742795104474.324216 ?21.06180692 0.11079926 ?125.1323202 0.853769015475.098888 ?18.72632807 0.7689708 ? 125.1400455 0.991577541472.708781 ?21.18145004 1.53044597 ?126.206574 ?0.894496186261.054388 ?196.4845601 2.85653651 ?126.4870562 0.884401301261.104845 ?196.6365273 2.96048717 ?126.8060731 0.840895112260.23671 ? 197.1606291 2.73990119 ?128.0764361 0.873334209261.085155 ?196.6737482 2.69219319 ?128.5328058 0.97339396812.009559 ? 160.8273903 0.89371542 ?129.4377345 0.81286608511.849503 ? 160.841293 ?1.14120928 ?129.6794689 0.76862943212.345148 ? 160.5244702 1.28818423 ?129.8214878 0.82705746111.135317 ? 160.7668114 1.65208029 ?130.7028618 0.78207886631.623888 ? 130.3067685 2.1127655 ? 132.5014859 0.83336975327.170348 ? 129.6318075 1.40646722 ?132.5051924 0.88825451431.403392 ? 130.7047954 2.29731991 ?132.8479736 0.86039237629.923974 ? 131.9784448 1.92817547 ?133.6366443 0.81563264890.074671 ? 59.07610607 1.23271524 ?134.6497729 0.9620350387.906549 ? 54.82957282 0.65955499 ?135.3859154 0.7901046289.899048 ? 57.83154064 0.30141145 ?135.5092119 0.820008915276.323019 ?6.86787982 ?1.7776151 ? 135.5215818 0.855317054275.970301 ?7.91419119 ?3.21748128 ?135.6636361 0.718547414275.727285 ?8.3243395 ? 1.94806409 ?136.057032 ?0.769410166276.514291 ?7.01085361 ?1.43467439 ?137.343003 ?0.735545797330.040302 ?144.5877302 0.66277381 ?137.4281315 0.729634011324.893213 ?146.4365159 0.88234134 ?137.6037721 0.967082637291.11468 ? 49.33367767 2.47072766 ?138.7895341 0.710016723293.43458 ? 48.62581312 1.98062144 ?139.3682232 0.951710498250.764567 ?198.5016519 0.85846877 ?140.0507716 0.852180017253.539089 ?201.132831 ?1.49089404 ?140.9996563 0.734114932253.512945 ?201.0537249 2.4727616 ? 141.0409587 0.847133697253.542791 ?201.2490377 1.98635162 ?142.6391569 0.879832516257.795509 ?216.9359492 0.78064425 ?145.1118214 0.72706484257.764285 ?216.4872431 2.80925094 ?145.1624047 0.99346721257.818943 ?216.6897931 2.33814072 ?145.9038514 0.895905632257.774863 ?216.6051295 2.44114347 ?145.9367341 0.838339638367.514438 ?31.4793139 ?0.78736947 ?146.1964166 0.959127433367.588968 ?31.4867048 ?0.96941256 ?146.2887533 0.778848722369.492049 ?30.48020726 2.4794555 ? 150.0217156 0.947188883143.865075 ?233.3690032 1.67318663 ?150.4491923 0.798692592144.098544 ?234.3763707 0.23773927 ?150.5166887 0.982390159218.32888 ? 216.7083106 2.74041746 ?151.0604421 0.773232421325.353164 ?143.7297267 2.96706415 ?151.763207 ?0.98713305326.419993 ?143.5201895 3.63452168 ?152.3832321 0.853247489325.936613 ?144.5316032 2.32157168 ?153.3589663 0.869373958325.810082 ?144.356522 ?4.39008693 ?153.4582455 0.99811483931.910325 ? 124.5598197 2.33494244 ?153.6579228 0.93129518231.351707 ? 125.4332729 2.30507449 ?154.0737073 0.79414057631.574903 ? 124.0463483 0.75565309 ?154.0886993 0.71736178732.54375 ? ?122.7135364 2.18675079 ?154.2861579 0.71322213890.008543 ? 124.8990934 1.97911207 ?154.3444858 0.94388319190.28441 ? ?126.6897782 1.01474716 ?154.9277926 0.82362198387.735243 ? 125.8623578 3.00304403 ?155.2644112 0.815248951260.385862 ?96.59499166 3.96772436 ?156.995524 ?0.85693796259.739291 ?97.04823338 2.61008235 ?157.5583662 0.96764469260.311284 ?96.68968926 4.22429753 ?157.6724828 0.821776192260.229276 ?95.34657991 2.54473831 ?157.7533106 0.881316669260.212422 ?187.7862368 4.31051589 ?157.9162288 0.728441067260.231256 ?188.2226327 3.3502332 ? 158.0074879 0.800794383261.545309 ?191.0387749 3.93897914 ?158.0767802 0.743452552272.998243 ?214.0871297 0.58707332 ?158.0785985 0.773464159272.69374 ? 214.5296828 1.42084384 ?159.6240869 0.813691498274.126863 ?212.7891744 0.26609394 ?159.9565838 0.781095884367.90561 ? 15.41286762 2.95145208 ?160.5243755 0.76467979367.864872 ?15.25877454 2.64007335 ?161.3173639 0.890119333367.649781 ?19.91579374 3.97005021 ?161.9414598 0.939914671148.118458 ?177.8767452 0.7438971 ? 162.0120391 0.762554208147.655051 ?176.9144773 1.3703557 ? 162.030937 ?0.968876858148.050091 ?176.9031162 1.30790609 ?162.3061767 0.923712841147.649022 ?175.9846377 0.01212553 ?162.6304654 0.860915742356.818492 ?67.21939123 1.76786772 ?164.2579604 0.990989558355.622664 ?68.75829882 3.19659511 ?164.3880109 0.869464951355.844738 ?68.88550929 4.36517304 ?164.7900766 0.76530697108.71847 ? 215.0266242 1.98752526 ?166.393087 ?0.957328986109.014859 ?214.6488939 3.20229933 ?167.6177713 0.958599795109.164433 ?215.2627269 1.93777216 ?167.8951075 0.793990658108.131203 ?215.0862499 2.35653921 ?168.2758637 0.798095263196.231361 ?70.49924437 1.97858279 ?168.4511479 0.952004021197.737244 ?72.88240664 0.65482871 ?169.5036831 0.847759836339.257305 ?120.888616 ?1.34736322 ?169.6356306 0.715570745340.781081 ?117.0187847 2.51971051 ?169.6790878 0.933405511338.606336 ?121.5834442 1.80270464 ?170.3047686 0.828001716338.041063 ?120.7029464 1.73078138 ?170.3913998 0.783988564338.99619 ? 35.10033383 2.97337925 ?170.4444717 0.800052404337.200856 ?33.51899806 1.09814538 ?170.613345 ?0.810081986336.985755 ?34.21892728 0.24128014 ?170.8469088 0.938437723220.803763 ?53.14430613 1.29837937 ?170.8645578 0.711607236221.630219 ?52.1940613 ?1.79796509 ?171.6146056 0.91800080198.635642 ? 121.5862813 2.9432507 ? 171.8511343 0.96180533898.382482 ? 121.1350972 1.85599348 ?171.9082703 0.78574443595.692992 ? 121.8135249 2.76335185 ?172.186239 ?0.89705477895.455554 ? 121.1536975 3.06349446 ?172.3154888 0.76956598829.902259 ? 220.4663988 0.032004 ? ?172.6212011 0.88658618228.41221 ? ?220.079011 ?0.64563437 ?172.71164 ? 0.7225371328.608348 ? 219.9848542 0.81174981 ?173.474008 ?0.99002676328.837549 ? 219.7118007 0.88414209 ?176.6881568 0.882990987417.469016 ?60.71793319 3.13009015 ?178.4274218 0.815114554420.412299 ?59.95963986 3.77420788 ?178.5608842 0.709170932417.835488 ?61.34888422 3.412701 ? ?179.0698474 0.957269676266.303184 ?148.8628134 4.14332284 ?179.975606 ?0.881062956266.264066 ?149.8292293 4.17012164 ?180.080254 ?0.954352122290.584215 ?94.18249675 2.09946968 ?180.3264641 0.851384874211.043848 ?164.8354141 0.38617853 ?180.4780309 0.702373251394.665914 ?165.8533229 2.94896243 ?180.6401804 0.975721953396.948844 ?164.3185096 2.95721695 ?181.189757 ?0.823211439394.152446 ?166.1863908 2.85283338 ?181.4459117 0.919709724355.861861 ?151.482828 ?1.79907458 ?181.5735067 0.745331584355.604564 ?151.2328554 1.42786694 ?182.0786425 0.944569983355.977914 ?151.7258945 2.60632787 ?182.2734472 0.9728807655.193224 ? 70.13457335 1.95421619 ?182.4681836 0.93338273855.121245 ? 70.26190069 1.7134954 ? 182.7419885 0.927136941466.029024 ?43.60374817 3.02745392 ?183.048289 ?0.821559257466.713681 ?43.04071215 3.34442703 ?183.0495735 0.910570324361.343579 ?38.84946077 4.09011265 ?183.1337707 0.869638281107.494724 ?224.061154 ?0.64225969 ?184.3347164 0.875420906109.403587 ?222.7703059 1.02129489 ?184.5405119 0.80347438108.536435 ?221.8397702 1.32737534 ?185.2302114 0.911269972108.966261 ?223.5009692 0.64308213 ?185.599194 ?0.748259104319.258848 ?64.01371204 4.34421863 ?185.7281496 0.70045418321.53673 ? 62.05801435 4.02840039 ?185.9683567 0.868600256320.136879 ?62.7561261 ?2.02796518 ?186.1012058 0.863945237426.321536 ?79.57156783 1.80279196 ?186.1655452 0.865248329425.254692 ?80.84699203 0.53246863 ?186.351376 ?0.908361028424.301716 ?81.17660654 0.05602379 ?186.4132518 0.978248228424.827296 ?81.04033515 1.33209986 ?186.4734765 0.983263093119.807247 ?187.958236 ?3.33382966 ?186.7652667 0.970978999120.210092 ?189.4849366 2.84489764 ?187.4376306 0.881231886120.205569 ?189.1727403 4.18836325 ?187.4622579 0.977862927247.808605 ?146.4244449 0.83110586 ?188.5004803 0.735083878249.294833 ?144.1907226 1.22128356 ?188.962155 ?0.802240452250.204516 ?146.4749518 1.7944476 ? 189.3051254 0.711019133334.654137 ?11.15448488 3.46662664 ?189.8126837 0.861510955333.659862 ?11.64954098 2.1332473 ? 190.1436423 0.92116864333.427405 ?10.95652538 2.75561873 ?191.3076606 0.7543667519.482643 ? ?85.46858555 1.15438219 ?191.3293578 0.8278739989.378643 ? ?85.45893223 2.23185957 ?191.4270999 0.7294503879.333447 ? ?84.55839727 1.36554428 ?192.1174705 0.79096647439.424485 ?237.4993259 0.59464444 ?192.4302016 0.934036784438.638525 ?238.1309002 0.47642958 ?192.835047 ?0.861088125439.977322 ?237.950318 ?1.51017279 ?193.0183715 0.93072143438.636146 ?237.9862702 1.3178479 ? 193.2070887 0.891683094330.410302 ?62.51368701 2.99926551 ?193.8201965 0.967944474329.790522 ?62.17494892 2.86913557 ?194.8657309 0.718207116329.460954 ?62.13150555 3.26717085 ?195.1562923 0.752731464474.563651 ?69.88329745 4.03771076 ?195.1657446 0.824899558285.627382 ?72.98472026 1.95847784 ?196.1019459 0.921937552286.820235 ?72.90395374 1.26502975 ?196.2494223 0.967886438236.897161 ?134.567653 ?1.15564329 ?196.4295919 0.707755992234.806852 ?133.6690276 0.210115 ? ?196.5220457 0.741268909233.53859 ? 132.9487054 2.28750244 ?196.5612547 0.82722623277.005222 ?47.68301903 4.36155011 ?196.6331458 0.929370035277.336998 ?44.11638043 3.06712344 ?197.5726448 0.857331156277.800836 ?43.03107739 3.70528439 ?197.5837294 0.926344408276.793356 ?44.16753185 3.20462984 ?197.9290181 0.750939533165.177531 ?248.6222625 0.3374573 ? 197.9766126 0.901818102164.463612 ?249.5902955 1.32364566 ?198.1684532 0.885595823161.499292 ?251.3536746 1.75217305 ?198.2615641 0.702053827440.799878 ?176.1199082 3.19808685 ?198.3114499 0.922067657441.798136 ?176.5611422 2.98843581 ?198.9449421 0.997520643441.027104 ?176.7791779 3.08648705 ?199.572324 ?0.738454407"
y1 <- read.table(text=zz, header = TRUE)
zzz <- " longitude ?latitude ? ?depth ? time ? ?magnitude277.728371 ?139.925845 ?0.75103658 ?26.40786514 0.943718276426.087586 ?168.903095 ?0.2957441 ? 0.241456485 0.759137864331.549444 ?74.168092 ? 0.55140397 ?66.51363095 0.77617643393.078983 ? 78.588053 ? 0.15328453 ?104.9418546 0.834896464492.359229 ?11.082291 ? 0.08173915 ?111.3391451 0.87479811986.85704 ? ?42.34973 ? ?0.23081904 ?152.8098572 0.878111793128.038949 ?73.935782 ? 0.66160123 ?157.8933315 0.990100773295.300125 ?1.935765 ? ?0.49789785 ?159.9134319 0.842815655294.688309 ?1.024583 ? ?0.44789667 ?165.7092358 0.886545275221.246937 ?151.217171 ?0.6337224 ? 167.6213491 0.885163617111.240376 ?156.04214 ? 0.55752237 ?171.2039395 0.88527352625.929383 ? 136.975153 ?0.0271747 ? 172.6574772 0.812214826415.726989 ?158.482975 ?0.37340509 ?184.3767148 0.9083717473.921877 ? 60.031908 ? 0.15224511 ?189.6429637 0.7914032288.811256 ? ?124.676545 ?0.26806101 ?193.7498013 0.813638308"y2 <- read.table(text=zzz, header = TRUE)
evpts1 <-do.call(expand.grid, ?lapply(y1,quantile, prob=c(.1,.15,.2,.25,.3,.35,.4,.45,.5,.55,.6,.65,.7,.75,.8, .85,.9,.95)))hat1 <- kde(y1, eval.points= evpts1)
evpts2 <-do.call(expand.grid, ?lapply(y2,quantile, prob=c(.1,.15,.2,.25,.3,.35,.4,.45,.5,.55,.6,.65,.7,.75,.8, .85,.9,.95)))hat2 <- kde(y2, eval.points= evpts2)
str(hat1)str(hat2)
integrand1 <- function(p){hat1(p,y1)+hat2(p,y2)}
Vintegrand <- Vectorize(integrand1)
integrate( Vintegrand, lower = 0, upper = t)


But it gives me error.?I appreciate any help in advance.