Evaluate the integral from

Question

[sqrt(pi/2), sqrt(pi)] of x^3*cos(x^2) by first making a substitution and then using integration by parts.

I let u = x^2 and du= 2x dx but then it doesn't equal that in the equation?

Answer 1

∫x^3 cos(x^2) dx
If you let u=x^2, you have du = 2x dx and the integral is
1/2 ∫[π/2,π] u cos(u) du

Now you can tackle that using integration by parts.