What did I do wrong?

The correct answer is

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- Jan 25th 2010, 10:14 AMMike9182Trig Substitution
What did I do wrong?

The correct answer is - Jan 25th 2010, 10:23 AMJhevon
- Jan 25th 2010, 10:32 AMMike9182
I set up a triangle and put the three main trig functions I found in my post, I just didn't place the triangle itself in my post because I wasn't sure how to do so using the latex editor.

- Jan 25th 2010, 10:32 AMKrizalid
- Jan 25th 2010, 10:48 AMJhevon
you set up the triangle

*after*you see what equation you should use. you should have seen that and set up the triangle based on that. then you wouldn't have this business. be sure to review trig sub so you know what equation to start with and hence how to set up the*right*triangle (no pun intended, well, maybe a little :D)

Haha, i know. i hate trig sub as well. This is what i thought of when i first saw the integral (then i sighed, grit my teeth and did what the OP asked for)

Let and the integral becomes

is there an easier way? - Jan 25th 2010, 11:00 AMMike9182
I set up the triangle so that the hypotenuse was , the adjacent angle to theta was , and the opposite angle to theta was . I'm guessing that when the triangle is set up the constant should be placed adjacent to theta when possible in order to make the process of working the problem out easier. Is this correct?

- Jan 25th 2010, 11:09 AMJhevon
no, you don't decide where the things go. your equation does.

you had the expression

this is of the form . the proper trig sub is

So that is here.

This means that which means that:

Your acute angle is

The opposite side is

The adjacent side is and

The hypotenuse is

The radical expression is not always the hypotenuse, our expression dictated where we put stuff