Definite and Indefinite Integrals
Hello,
I have two handout problem from my professor that I can't quite figure out on my own. These two problems are NOT homework problems.
So we have the integral of (sin(x))^2*(cos(x))^3 dx. The hint I was given was to rewrite it as the integral (sin(x))^2*(1-(sin(x))^2*(cos(x)) dx. Is that even allowed? There is no trig identity where I am allowed to do this... This problem is a Definite integral from a=pi/4 to b=pi/2.
The other problem I was having trouble with is to take the indefinite integral of arc sec(sqrx) dx. The hint my professor gave me was to let: u=arc sec(sqrx) and dv=dx. I think I am just having trouble with some algebra in this problem. If you gentlemen figure it out could you please post a picture of the problem worked out? Thank you.