If f(2)=6 and f`(x)=sinx^3, find f(4).

Question

i don’t know what the integral of sin(x^3) is and i can’t move onto the next steps

Answer 1

I don't know the integral of sin³x either...but I looked it up.

The integral of sin³x = (-1/3) cos x (sin²x + 2) + C.

But to be fair I think you integrate sin³x this way.

Start with cos²x - sin²x = cos 2x

Then sin²x = (1-cos 2x)/2

sin³x = (1/2)(sin x - sin x cos 2x)

and you should be able to integrate sin x cos 2x by parts.

Sorry, not quite right:

The integral is correct, but you get it by integrating sin³x as sin x sin²x dx by parts.