Question

can someone check my work for this intregration question? I have 3 solutions but can't figure out which is right haha ( the picture is attached below in the comment box)

Answer 1

One way to do it is to differentiate the solution and see if it gives you the original integral. If it does then you are right.

Answer 2

There is a much simpler way to integrate that function without using trig substitution.

Answer 3

i know but unfortunately she said we have to use trig substitution :/

Answer 4

i'm just unsure if my work for method one is right so i tried method 2, but i'm not sure if either are right haha

Answer 5

Do you understand that integration and differentiation are inverses of each other?

Answer 6

method 1 and 3 look ok

in method 2, cos^2(\(\theta\)) is not dx

Answer 7

oh i don't know what i did there haha thanks for catching that phi! and thanks for your help Isaiah i don't know how i didn't think of checking that way haha

Answer 8

Is a must to use trig substitution?

Answer 9

yup :(

Answer 10

That's not even necessary because the integrand can be simplified algebraically.