(a) If we use the substitution t = 6tan(θ), then which of the following integrals is equivalent to ?
1
(b) Use the integral in part (a) to evaluate
Please show all steps and tank you!
Hello, choshiwara!
(a) If we use the substitution ,
then which of the following integrals is equivalent to: .
Let:
Substitute: . . . . answer choice (1)
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
We have: .
. . .[1]
Back-substitute: .
So is in a right triangle with: .
Using Pythagorus, we find that: .
. . Hence: .
Therefore, [1] becomes: .