0
$\begingroup$

I have a list given by:

CVlist = {{2., 0.0051366}, {1.99, 0.0055522}, {1.98, 0.0055776}, {1.97, 
  0.0056172}, {1.96, 0.0056914}, {1.95, 0.005718}, {1.94, 
  0.0058168}, {1.93, 0.005763}, {1.92, 0.0058166}, {1.91, 
  0.005825}, {1.9, 0.005811}, {1.89, 0.005855}, {1.88, 
  0.005904}, {1.87, 0.005982}, {1.86, 0.0059608}, {1.85, 
  0.0059964}, {1.84, 0.0060254}, {1.83, 0.0060182}, {1.82, 
  0.0060702}, {1.81, 0.0060804}, {1.8, 0.0061024}, {1.79, 
  0.0061354}, {1.78, 0.006144}, {1.77, 0.0062208}, {1.76, 
  0.006249}, {1.75, 0.0062654}, {1.74, 0.0062854}, {1.73, 
  0.0063462}, {1.72, 0.0063774}, {1.71, 0.0063908}, {1.7, 
  0.0064476}, {1.69, 0.00646}, {1.68, 0.00649}, {1.67, 
  0.0065176}, {1.66, 0.0065526}, {1.65, 0.0065642}, {1.64, 
  0.0066418}, {1.63, 0.0066678}, {1.62, 0.00672}, {1.61, 
  0.0067618}, {1.6, 0.006808}, {1.59, 0.0068496}, {1.58, 
  0.0068586}, {1.57, 0.0069134}, {1.56, 0.0069142}, {1.55, 
  0.0069684}, {1.54, 0.0070046}, {1.53, 0.007064}, {1.52, 
  0.0070684}, {1.51, 0.0071524}, {1.5, 0.0071902}, {1.49, 
  0.0072572}, {1.48, 0.0072908}, {1.47, 0.007335}, {1.46, 
  0.0073972}, {1.45, 0.0074334}, {1.44, 0.0074576}, {1.43, 
  0.0075808}, {1.42, 0.0076208}, {1.41, 0.0076606}, {1.4, 
  0.007715}, {1.39, 0.0077636}, {1.38, 0.0078378}, {1.37, 
  0.0078974}, {1.36, 0.0079532}, {1.35, 0.0080048}, {1.34, 
  0.0080706}, {1.33, 0.0081186}, {1.32, 0.0081862}, {1.31, 
  0.0082282}, {1.3, 0.0083004}, {1.29, 0.0083812}, {1.28, 
  0.008444}, {1.27, 0.0085116}, {1.26, 0.0085498}, {1.25, 
  0.0086192}, {1.24, 0.0086868}, {1.23, 0.0087308}, {1.22, 
  0.0088088}, {1.21, 0.0088748}, {1.2, 0.0089128}, {1.19, 
  0.0089986}, {1.18, 0.0090664}, {1.17, 0.0091242}, {1.16, 
  0.0091788}, {1.15, 0.0092592}, {1.14, 0.0093156}, {1.13, 
  0.0093864}, {1.12, 0.0094594}, {1.11, 0.0095296}, {1.1, 
  0.0095998}, {1.09, 0.0096544}, {1.08, 0.0097304}, {1.07, 
  0.0098094}, {1.06, 0.0098674}, {1.05, 0.0099384}, {1.04, 
  0.010011}, {1.03, 0.010075}, {1.02, 0.0101694}, {1.01, 
  0.010244}, {1., 0.0103182}, {0.99, 0.0103704}, {0.98, 
  0.0104508}, {0.97, 0.0105082}, {0.96, 0.010587}, {0.95, 
  0.0106396}, {0.94, 0.0107312}, {0.93, 0.0107744}, {0.92, 
  0.0108432}, {0.91, 0.0109068}, {0.9, 0.0109622}, {0.89, 
  0.011014}, {0.88, 0.0110524}, {0.87, 0.0111198}, {0.86, 
  0.0111468}, {0.85, 0.011192}, {0.84, 0.011238}, {0.83, 
  0.0112706}, {0.82, 0.011328}, {0.81, 0.01137}, {0.8, 
  0.0114086}, {0.79, 0.0114524}, {0.78, 0.0114832}, {0.77, 
  0.0115342}, {0.76, 0.0115648}, {0.75, 0.011609}, {0.74, 
  0.0116402}, {0.73, 0.0116838}, {0.72, 0.0116968}, {0.71, 
  0.0117136}, {0.7, 0.0117558}, {0.69, 0.011779}, {0.68, 
  0.0117914}, {0.67, 0.0118158}, {0.66, 0.0118342}, {0.65, 
  0.011848}, {0.64, 0.0118592}, {0.63, 0.0118608}, {0.62, 
  0.0118654}, {0.61, 0.0118728}, {0.6, 0.0118744}, {0.59, 
  0.0118906}, {0.58, 0.0118798}, {0.57, 0.0118866}, {0.56, 
  0.011877}, {0.55, 0.0118772}, {0.54, 0.011873}, {0.53, 
  0.011871}, {0.52, 0.011868}, {0.51, 0.0118644}, {0.5, 
  0.0118614}, {0.49, 0.0118546}, {0.48, 0.0118518}, {0.47, 
  0.011842}, {0.46, 0.011844}, {0.45, 0.0118474}, {0.44, 
  0.011838}, {0.43, 0.0118362}, {0.42, 0.011834}, {0.41, 
  0.0118322}, {0.4, 0.011822}, {0.39, 0.011821}, {0.38, 
  0.011817}, {0.37, 0.0118126}, {0.36, 0.0118072}, {0.35, 
  0.011801}, {0.34, 0.0117946}, {0.33, 0.0117904}, {0.32, 
  0.0117874}, {0.31, 0.011776}, {0.3, 0.0117796}, {0.29, 
  0.0117726}, {0.28, 0.0117622}, {0.27, 0.0117582}, {0.26, 
  0.011757}, {0.25, 0.0117482}, {0.24, 0.0117418}, {0.23, 
  0.0117382}, {0.22, 0.0117306}, {0.21, 0.0117248}, {0.2, 
  0.0117178}, {0.19, 0.0117122}, {0.18, 0.0117036}, {0.17, 
  0.0117012}, {0.16, 0.0116852}, {0.15, 0.011689}, {0.14, 
  0.0116768}, {0.13, 0.0116694}, {0.12, 0.0116608}, {0.11, 
  0.0116496}, {0.1, 0.0116456}, {0.09, 0.0116418}, {0.08, 
  0.0116316}, {0.07, 0.011622}, {0.06, 0.0116136}, {0.05, 0.0116072}, 
 {0.04, 0.0116006}, {0.03, 0.011587}, {0.0200001, 
  0.0115788}, {0.0099999, 0.011571}, {0., 0.011557}, {-0.0099999, 
  0.0115484}, {-0.0199999, 0.0115378}, {-0.0299999, 
  0.0115246}, {-0.0399999, 0.0115168}, {-0.0499999, 
  0.0115046}, {-0.0599999, 0.0114936}, {-0.0699999, 
  0.0114828}, {-0.0799999, 0.011473}, {-0.0899999, 
  0.0114584}, {-0.0999999, 0.0114446}, {-0.11, 0.0114318}, {-0.12, 
  0.0114206}, {-0.13, 0.0114024}, {-0.14, 0.0113854}, {-0.15, 
  0.0113744}, {-0.16, 0.0113562}, {-0.17, 0.0113412}, {-0.18, 
  0.0113236}, {-0.19, 0.011308}, {-0.2, 0.0112946}, {-0.21, 
  0.0112698}, {-0.22, 0.0112504}, {-0.23, 0.0112394}, {-0.24, 
  0.0112112}, {-0.25, 0.0111918}, {-0.26, 0.0111672}, {-0.27, 
  0.0111444}, {-0.28, 0.0111276}, {-0.29, 0.0110976}, {-0.3, 
  0.011069}, {-0.31, 0.0110492}, {-0.32, 0.0110144}, {-0.33, 
  0.0109964}, {-0.34, 0.0109604}, {-0.35, 0.010924}, {-0.36, 
  0.0109026}, {-0.37, 0.0108632}, {-0.38, 0.0108254}, {-0.39, 
  0.010791}, {-0.4, 0.0107526}, {-0.41, 0.0107194}, {-0.42, 
  0.010673}, {-0.43, 0.0106238}, {-0.44, 0.010586}, {-0.45, 
  0.0105284}, {-0.46, 0.0104828}, {-0.47, 0.0104354}, {-0.48, 
  0.0103708}, {-0.49, 0.010321}, {-0.5, 0.0102592}, {-0.51, 
  0.0101834}, {-0.52, 0.010137}, {-0.53, 0.010051}, {-0.54, 
  0.0099804}, {-0.55, 0.00991}, {-0.56, 0.00982}, {-0.57, 
  0.0097482}, {-0.58, 0.0096506}, {-0.59, 0.0095536}, {-0.6, 
  0.0094808}, {-0.61, 0.0093546}, {-0.62, 0.0092536}, {-0.63, 
  0.0091526}, {-0.64, 0.0090188}, {-0.65, 0.0089182}, {-0.66, 
  0.0087808}, {-0.67, 0.0086192}, {-0.68, 0.0084804}, {-0.69, 
  0.0083324}, {-0.7, 0.0081794}, {-0.71, 0.0080284}, {-0.72, 
  0.0078636}, {-0.73, 0.007694}, {-0.74, 0.0075248}, {-0.75, 
  0.0073638}, {-0.76, 0.0071656}, {-0.77, 0.0069632}, {-0.78, 
  0.006755}, {-0.79, 0.0065226}, {-0.8, 0.006302}, {-0.81, 
  0.0060902}, {-0.82, 0.0058832}, {-0.83, 0.0056596}, {-0.84, 
  0.0054396}, {-0.85, 0.0052286}, {-0.86, 0.0050156}, {-0.87, 
  0.0048056}, {-0.88, 0.0046058}, {-0.89, 0.0043912}, {-0.9, 
  0.0041728}, {-0.91, 0.003957}, {-0.92, 0.0037312}, {-0.93, 
  0.0035268}, {-0.94, 0.0033312}, {-0.95, 0.003159}, {-0.96, 
  0.0029828}, {-0.97, 0.00282}, {-0.98, 0.0026606}, {-0.99, 
  0.0025142}, {-1., 0.0023834}, {-1.01, 0.0022734}, {-1.02, 
  0.0021412}, {-1.03, 0.0020166}, {-1.04, 0.0018933}, {-1.05, 
  0.00177686}, {-1.06, 0.00167707}, {-1.07, 0.00158495}, {-1.08, 
  0.001501}, {-1.09, 0.00141759}, {-1.1, 0.00134738}, {-1.11, 
  0.00127342}, {-1.12, 0.00120972}, {-1.13, 0.00115754}, {-1.14, 
  0.00109679}, {-1.15, 0.00103776}, {-1.16, 0.000978561}, {-1.17, 
  0.000931304}, {-1.18, 0.000877683}, {-1.19, 0.00082866}, {-1.2, 
  0.000784214}, {-1.21, 0.000741349}, {-1.22, 0.000701488}, {-1.23, 
  0.000666435}, {-1.24, 0.000633176}, {-1.25, 0.000605046}, {-1.26, 
  0.000574798}, {-1.27, 0.000551643}, {-1.28, 0.000523257}, {-1.29, 
  0.000496835}, {-1.3, 0.000474573}, {-1.31, 0.00045013}, {-1.32, 
  0.0004315}, {-1.33, 0.000410219}, {-1.34, 0.00039705}, {-1.35, 
  0.00038075}, {-1.36, 0.000363841}, {-1.37, 0.000355021}, {-1.38, 
  0.000342366}, {-1.39, 0.000330596}, {-1.4, 0.000325972}, {-1.41, 
  0.000312141}, {-1.42, 0.000304022}, {-1.43, 0.000294081}, {-1.44, 
  0.00028828}, {-1.45, 0.000278519}, {-1.46, 0.000273236}, {-1.47, 
  0.000267597}, {-1.48, 0.000261126}, {-1.49, 0.000256398}, {-1.5, 
  0.000251367}, {-1.51, 0.000237384}, {-1.52, 0.000237514}, {-1.53, 
  0.000238657}, {-1.54, 0.000231272}, {-1.55, 0.000222174}, {-1.56, 
  0.000225314}, {-1.57, 0.000221738}, {-1.58, 0.000219292}, {-1.59, 
  0.000213942}, {-1.6, 0.000212358}, {-1.61, 0.000209701}, {-1.62, 
  0.000203257}, {-1.63, 0.000204665}, {-1.64, 0.00019744}, {-1.65, 
  0.000200486}, {-1.66, 0.000197822}, {-1.67, 0.000199524}, {-1.68, 
  0.000190081}, {-1.69, 0.000192646}, {-1.7, 0.000188788}, {-1.71, 
  0.000194794}, {-1.72, 0.000190018}, {-1.73, 0.000184759}, {-1.74, 
  0.000181173}, {-1.75, 0.000183473}, {-1.76, 0.000178789}, {-1.77, 
  0.000181179}, {-1.78, 0.000178337}, {-1.79, 0.00018076}, {-1.8, 
  0.000174888}, {-1.81, 0.000176043}, {-1.82, 0.000176726}, {-1.83, 
  0.000171554}, {-1.84, 0.000176347}, {-1.85, 0.000173084}, {-1.86, 
  0.000177068}, {-1.87, 0.000172401}, {-1.88, 0.000175262}, {-1.89, 
  0.000171405}, {-1.9, 0.000168473}, {-1.91, 0.000171686}, {-1.92, 
  0.000170907}, {-1.93, 0.000170068}, {-1.94, 0.000165658}, {-1.95, 
  0.000166828}, {-1.96, 0.000164397}, {-1.97, 0.000167235}, {-1.98, 
  0.000163341}, {-1.99, 0.000163704}, {-2., 0.000159774}, {-2.01, 
  0.000163869}, {-2.02, 0.000165949}, {-2.03, 0.000161515}, {-2.04, 
  0.000159285}, {-2.05, 0.000166547}, {-2.06, 0.00016665}, {-2.07, 
  0.00015814}, {-2.08, 0.00016321}, {-2.09, 0.000162045}, {-2.1, 
  0.000160948}, {-2.11, 0.000161541}, {-2.12, 0.000164668}, {-2.13, 
  0.000159375}, {-2.14, 0.000159323}, {-2.15, 0.000156826}, {-2.16, 
  0.000160236}, {-2.17, 0.000156728}, {-2.18, 0.000159855}, {-2.19, 
  0.000160659}, {-2.2, 0.000158737}, {-2.21, 0.000157678}, {-2.22, 
  0.00015855}, {-2.23, 0.000154608}, {-2.24, 0.000158322}, {-2.25, 
  0.000152283}, {-2.26, 0.000158707}, {-2.27, 0.0001538}, {-2.28, 
  0.000153039}, {-2.29, 0.000157154}, {-2.3, 0.000157532}, {-2.31, 
  0.000158076}, {-2.32, 0.000149937}, {-2.33, 0.000153116}, {-2.34, 
  0.000154896}, {-2.35, 0.00015641}, {-2.36, 0.000159982}, {-2.37, 
  0.00015816}, {-2.38, 0.0001494}, {-2.39, 0.000157449}, {-2.4, 
  0.000154594}, {-2.41, 0.00015496}, {-2.42, 0.000153543}, {-2.43, 
  0.000156022}, {-2.44, 0.00015341}, {-2.45, 0.000151543}, {-2.46, 
  0.000152498}, {-2.47, 0.000151152}, {-2.48, 0.000151321}, {-2.49, 
  0.000155392}, {-2.5, 0.000153984}, {-2.51, 0.00015666}, {-2.52, 
  0.000151489}, {-2.53, 0.000153472}, {-2.54, 0.000154703}, {-2.55, 
  0.000151233}, {-2.56, 0.000152223}, {-2.57, 0.000157624}, {-2.58, 
  0.00015381}, {-2.59, 0.000153716}, {-2.6, 0.000147252}, {-2.61, 
  0.000148681}, {-2.62, 0.000154699}, {-2.63, 0.000151271}, {-2.64, 
  0.000148417}, {-2.65, 0.000150262}, {-2.66, 0.000146912}, {-2.67, 
  0.000148166}, {-2.68, 0.000147649}, {-2.69, 0.000154523}, {-2.7, 
  0.000152326}, {-2.71, 0.00015228}, {-2.72, 0.000152544}, {-2.73, 
  0.000151545}, {-2.74, 0.00014943}, {-2.75, 0.000151607}, {-2.76, 
  0.000152598}, {-2.77, 0.000148502}, {-2.78, 0.000152791}, {-2.79, 
  0.00015181}, {-2.8, 0.000155151}, {-2.81, 0.000153198}, {-2.82, 
  0.000149564}, {-2.83, 0.000154169}, {-2.84, 0.000148498}, {-2.85, 
  0.000149023}, {-2.86, 0.000152966}, {-2.87, 0.000146125}, {-2.88, 
  0.000151339}, {-2.89, 0.000152582}, {-2.9, 0.000145544}, {-2.91, 
  0.000152714}, {-2.92, 0.00014943}, {-2.93, 0.000152399}, {-2.94, 
  0.000150816}, {-2.95, 0.000149864}, {-2.96, 0.000146683}, {-2.97, 
  0.000146814}, {-2.98, 0.000149168}, {-2.99, 0.000150392}, {-3., 
  0.000147305}, {-3.01, 0.000149189}, {-3.02, 0.000147218}, {-3.03, 
  0.000147623}, {-3.04, 0.000146495}, {-3.05, 0.000148891}, {-3.06, 
  0.000147972}, {-3.07, 0.000151707}, {-3.08, 0.000150167}, {-3.09, 
  0.000147372}, {-3.1, 0.000151506}, {-3.11, 0.000147476}, {-3.12, 
  0.000149721}, {-3.13, 0.000147067}, {-3.14, 0.000142604}, {-3.15, 
  0.000150872}, {-3.16, 0.000147654}, {-3.17, 0.000148984}, {-3.18, 
  0.000143861}, {-3.19, 0.000149885}, {-3.2, 0.000150197}, {-3.21, 
  0.00014712}, {-3.22, 0.000147592}, {-3.23, 0.000145668}, {-3.24, 
  0.000145555}, {-3.25, 0.000151055}, {-3.26, 0.000147672}, {-3.27, 
  0.000147423}, {-3.28, 0.000147998}, {-3.29, 0.000147161}, {-3.3, 
  0.000146688}, {-3.31, 0.000146498}, {-3.32, 0.000147699}, {-3.33, 
  0.000145035}, {-3.34, 0.000148967}, {-3.35, 0.000147651}, {-3.36, 
  0.000147369}, {-3.37, 0.000150596}, {-3.38, 0.000144972}, {-3.39, 
  0.000146561}, {-3.4, 0.000148868}, {-3.41, 0.0001415}, {-3.42, 
  0.000144211}, {-3.43, 0.000144588}, {-3.44, 0.000147619}, {-3.45, 
  0.000143777}, {-3.46, 0.000146242}, {-3.47, 0.000143249}, {-3.48, 
  0.000145719}, {-3.49, 0.000144735}, {-3.5, 0.000142692}, {-3.51, 
  0.000150164}, {-3.52, 0.000149834}, {-3.53, 0.000148119}, {-3.54, 
  0.000149415}, {-3.55, 0.000151121}, {-3.56, 0.000143085}, {-3.57, 
  0.000146686}, {-3.58, 0.000145502}, {-3.59, 0.000148152}, {-3.6, 
  0.000144023}, {-3.61, 0.000150704}, {-3.62, 0.000146199}, {-3.63, 
  0.000145112}, {-3.64, 0.000146634}, {-3.65, 0.000148036}, {-3.66, 
  0.000143444}, {-3.67, 0.000150514}, {-3.68, 0.000148373}, {-3.69, 
  0.000148859}, {-3.7, 0.000146234}, {-3.71, 0.000148675}, {-3.72, 
  0.00014706}, {-3.73, 0.000145674}, {-3.74, 0.000147024}, {-3.75, 
  0.000148471}, {-3.76, 0.00014958}, {-3.77, 0.000142535}, {-3.78, 
  0.000145124}, {-3.79, 0.000147338}, {-3.8, 0.000147988}, {-3.81, 
  0.00014669}, {-3.82, 0.000147192}, {-3.83, 0.000144477}, {-3.84, 
  0.000144017}, {-3.85, 0.000148101}, {-3.86, 0.000145787}, {-3.87, 
  0.000144286}, {-3.88, 0.000147316}, {-3.89, 0.000146842}, {-3.9, 
  0.000144345}, {-3.91, 0.000149818}, {-3.92, 0.000148809}, {-3.93, 
  0.000148019}, {-3.94, 0.000142107}, {-3.95, 0.000147857}, {-3.96, 
  0.000145532}, {-3.97, 0.000143592}, {-3.98, 0.000142888}, {-3.99, 
  0.000145381}, {-4., 0.000144193}};

The plot looks something like this: enter image description here

Now, I want to integrate over the $y$ values only till $x=0.5$ around which the y obtains maxima and then starts dropping. What is the best way to integrate from $y$ from $x=-4$ to $x=0.5$?

$\endgroup$
1

1 Answer 1

3
$\begingroup$

I don't know wheter this is the best way, but that direct approach works

Interpolation[CVlist]
NIntegrate[%[x], {x, -4, 0.5}, AccuracyGoal -> 5, PrecisionGoal -> 5]
(*0.0116836*)

Addition.

int = Interpolation[CVlist];
f[x_?NumericQ] :=NIntegrate[int[t], {t, -4, x}, AccuracyGoal -> 5, PrecisionGoal -> 5];
f[1]
(*0.021395*)
$\endgroup$
1
  • $\begingroup$ Actually I want to get the integrated value as a function of x $\endgroup$ Commented Feb 5, 2021 at 18:02

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