Trapezoidal rule to approximate an integral.

integrate_trapeze(x, y)

Arguments

x

a numerical vector, the discretization of the domain.

y

a numerical value, the discretization of the function to integrate.

Value

a numerical value, the approximation.

Examples

x <- seq(0,1,le=1e2)
integrate_trapeze(x,x^2)
#> [1] 0.3333503

integrate_trapeze(data1$grids[[1]],t(data1$x[[1]]))
#>   [1]  0.765079346 -0.523121394  0.110162421  0.511359289 -0.076194125
#>   [6]  0.447061420  1.195513927 -0.714186172  0.108260962 -0.453690367
#>  [11]  0.444751285  0.932100611  0.484307967  0.559383181  0.747189010
#>  [16]  0.130294931  0.742418349 -0.367985937  0.585063522  0.047428909
#>  [21]  0.833092171  0.699780729  0.204685357 -0.181267655 -0.405452489
#>  [26] -0.116764670 -0.338860486  0.723251161  0.151995527 -0.085662035
#>  [31]  0.135661583  0.751428785  1.236231229 -0.091728601  1.326770124
#>  [36]  0.807169443  0.651132111  0.471232361  0.743546958 -0.095618061
#>  [41] -0.350846179  0.526363005 -0.119156655  0.759310899  0.594419369
#>  [46]  0.394152962  0.043590128  0.118649164  0.039093021  0.953720396
#>  [51]  0.419098166  0.048841866  0.815175917  0.475707916  1.565346201
#>  [56]  0.247705062  0.716300292 -0.002235022 -0.117133144 -0.364707069
#>  [61]  0.341318004 -0.755102928 -0.018109197  0.030548350  0.465919302
#>  [66] -0.585647073  0.236361198  0.424777787 -0.019647527  1.126328518
#>  [71] -0.018765451  0.360326074  0.523242926  0.515121445  0.970761443
#>  [76] -0.214991107  0.723206670  0.914546246  0.475460418  0.115811401
#>  [81]  0.949779314  0.804449487  0.914315265 -0.009495039 -0.220266642
#>  [86]  0.782648023  0.419840231  0.487560509  0.552263538  0.473403065
#>  [91]  0.807408627  0.553560418  0.621720805  1.662158676 -0.183335683
#>  [96]  0.999037788  0.425226621  0.642306066  0.046729330  0.667871861