Evaluation of Integration without Loops

Hello all.

I have a mathematical expression takes the following form,

where C is known scalar, and or is known vector. The question here is, Does MATLAB have some functions to evaluate this integral function without using loops (I have the solution with for loop)?

I am trying to look for the minimum time the PC takes to evaluate the function becasue I am optimizing the scalar C against some objective function. For example, does conv() can help here by anyhow?

Thanks a lot,

Ahmad

Answer 1

[Ahmad Gad]

I fixed it using cumtrapz() function.

Answer 2

[madhan ravi]

help trapz

 TRAPZ  Trapezoidal numerical integration.
    Z = TRAPZ(Y) computes an approximation of the integral of Y via
    the trapezoidal method (with unit spacing).  To compute the integral
    for spacing different from one, multiply Z by the spacing increment.
 
    For vectors, TRAPZ(Y) is the integral of Y. For matrices, TRAPZ(Y)
    is a row vector with the integral over each column. For N-D
    arrays, TRAPZ(Y) works across the first non-singleton dimension.
 
    Z = TRAPZ(X,Y) computes the integral of Y with respect to X using the
    trapezoidal method. X can be a scalar or a vector with the same length
    as the first non-singleton dimension in Y. TRAPZ operates along this
    dimension. If X is scalar, then TRAPZ(X,Y) is equivalent to X*TRAPZ(Y).
 
    Z = TRAPZ(X,Y,DIM) or TRAPZ(Y,DIM) integrates across dimension DIM
    of Y. The length of X must be the same as size(Y,DIM)).
 
    Example:
        Y = [0 1 2; 3 4 5]
        trapz(Y,1)
        trapz(Y,2)
 
    Class support for inputs X, Y:
       float: double, single
 
    See also SUM, CUMSUM, CUMTRAPZ, INTEGRAL.

    Documentation for trapz
       doc trapz

    Other functions named trapz

       codistributed/trapz    gpuArray/trapz

[Ahmad Gad]

Is it possible to do it using a single trapz? I understand that I have to involve the trapz inside a loop becasue the upper limit of the integral is variable t.