Double integration with respect to same variable in defiinte range

How to double integrate an expression with same variable numerically(using Simson's rule) for example we have a function acceleration A=t*sint for t ranging from 0 to 1sec, how to find displacement by numerically integrating the function twice with respect to t.

Answer 1

[Rajat Tewari]

Hi Godas,

The solution to this problem can be achieved in 2 ways:

If you have Symbolic Toolbox, you can do this easily:

>> syms t;

>> f = t*sin(t);

>> result = int( int(f), [0 1])

>> vpa(result)

If you do not have symbolic toolbox, this can be done in following way:

>> format long

>> f = @(x,t) t.*sin(t)

>> y2 = @(x) x;

>> result = integral2(f2,0,1,0,y2);

Important Note: In second method, as you can see that I have put the lower limit of inside integral as 0 which is working for this case but if the result of first integral yields then it will become 1. Similarly, if it yields , then you have to use . Keep this in mind.

Hope it helps

[Godas Srikar]

Mr Tewari

Thank you