∫(√(64 - x^2)) / x dx
I must solve this using a sin substitution.
x = 8sinΘ
dx = 8cosΘ dΘ
Θ = arcsin(x/8)
The Attempt at a Solution
= ∫8cosΘ * (√(64 - 64sin^2Θ)) / 8sinΘ dΘ
= ∫(cosΘ * (√(64(1 - sin^2Θ))) / sinΘ dΘ
= ∫(cosΘ * (√(64cos^2Θ)) / sinΘ dΘ
= ∫8cos^2Θ / sinΘ dΘ
At this point, I didn't see any easy substitutions, like the rest of the problem set. So I thought there was a good chance I made an error. I checked to see if the answer to this integral was the same as the answer to the original integral, and saw that it wasn't. So somewhere up to this point, I made a mistake. After looking over my work, I don't see what I did wrong. Maybe it's just the integral calculator I'm using, I'm not sure.
Either way, I don't really know how to proceed with this problem. Sorry if the formatting is hard to read. I don't know the bbcode for posting these symbols properly and am in a rush at the moment.