# Trigonometric Integrals

• Jan 20th 2013, 11:25 AM
amthomasjr
Trigonometric Integrals
Attachment 26624

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 $\displaystyle \int 75cos^2 x sinx dx - \int (?) dx$ is really confusing me. Can someone explain what is happening?
• Jan 20th 2013, 11:34 AM
HallsofIvy
Re: Trigonometric Integrals
Don't you understand that this is not a question of "Calculus" but of "Algebra"? $\displaystyle sin(x)(1- cos^2(x))(cos(x))= sin(x)(cos(x)- cos^3(x))= sin(x)cos(x)- sin(x)cos^3(x)$.

I have used the "distributive law", a(b+ c)= ab+ ac, twice.
• Jan 20th 2013, 11:35 AM
christophina
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
• Jan 20th 2013, 12:00 PM
amthomasjr
Re: Trigonometric Integrals
I guess I didn't realize that $\displaystyle \int u-v=\int u - \int v$

Thank you both
• Jan 20th 2013, 12:05 PM
amthomasjr
Re: Trigonometric Integrals
$\displaystyle \int 75cos^2 x sin x dx - \int 75sin x cos^4 x$