1. ## Trigonometric Integrals

I need some help. I've watched a video that explained a similar problem, but it never showed any subtraction of integrals in the explanation. Nothing about subtracting integrals is in the textbook either.
Yes, this is homework. I'm not here for anyone to do it, but the $\int 75cos^2 x sinx dx - \int (?) dx$ is really confusing me. Can someone explain what is happening?

2. ## Re: Trigonometric Integrals

Don't you understand that this is not a question of "Calculus" but of "Algebra"? $sin(x)(1- cos^2(x))(cos(x))= sin(x)(cos(x)- cos^3(x))= sin(x)cos(x)- sin(x)cos^3(x)$.

I have used the "distributive law", a(b+ c)= ab+ ac, twice.

3. ## Re: Trigonometric Integrals

You're just expanding - I am not quite up to scratch with the LateX so....

Int(75 s(1-c^2)c^2) = Int(75 sc^2 - sc^4) = Int(75 sc^2) - Int(sc^4)
The part that with the ? is the part that I bolded

4. ## Re: Trigonometric Integrals

I guess I didn't realize that $\int u-v=\int u - \int v$

Thank you both

5. ## Re: Trigonometric Integrals

$\int 75cos^2 x sin x dx - \int 75sin x cos^4 x$