Trigonometric Integrals

**amthomasjr** · January 20th 2013, 11:25 AM

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?

**HallsofIvy** · January 20th 2013, 11:34 AM

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.

**christophina** · January 20th 2013, 11:35 AM

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

**amthomasjr** · January 20th 2013, 12:00 PM

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

Thank you both

**amthomasjr** · January 20th 2013, 12:05 PM

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

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