Need help with matlab code for below mentioned integrals

I want to know how to write the code for below two integrals

1.) If , then how to write the matlab code for .

2.) If , then how to write the matlab code for .

[Dyuman Joshi]

What have you tried yet? Please show your code.

[Nikhil]

@Dyuman Joshi I don't know from where to begin actually I was trying the inbuilt matlab function like trapz for trapizoidal rule and conv(f,g) for convolution but it didn't work. I guess these function work only if function is of single variable. Since in my case function is of two variable I don't know how to integrate wrt one variable.

[Dyuman Joshi]

conv and trapz only supports numeric data.

Are you sure you have to use trapezoidal rule? You can achieve the result of the integration without using it.

[Nikhil]

Okay Sir, if you know another way to calculate these two integral can you please help?

Answer 1

[Dyuman Joshi]

Note that you need symbolic toolbox to run this code -

syms a b x y tau
%Defining functions
r(a,b) = exp(-a-b);
f(a,x) = exp(-0.09*a) + (sin(0.05*x))^2;
K(x) = exp(-x^2)/sqrt(sym(pi));

P = int(r(a,tau)*f(tau,x), tau, 0, 50)

P = 

%To calculate the value of the integral for particular values of a and x
%use subs,
P_val = subs(P, [a,x], [1,0])

P_val = 

J = int(K(x-y)*f(a,y), y, 0, 50)

J = 

J_val=subs(J, [a,x], [1,0])

J_val = 

For J, int() is unable to compute the value of the definite integral. However, you can get the approximate numerical value by using vpa

J_valapprox=vpa(J_val)

J_valapprox = 

0.45758981203624906236445682215257