Post #3

Alrighty here we go...

First, I would like to list some identities that I need to learn:

sinx= 1/2 - 1/2cos2x
cosx= 1/2 + 1/2cos2x

cos^2x + sin^2x = 1
1 + tan^2x = sec^2x
1 + cot^2x = csc^2x

tanx = sinx/cosx
cotx = cosx/sinx

sin(2x) = 2sinxcosx

Well, we have been doing trig sub like all week. So let me try to explain it the best way I can since I haven't gotten the hang of it just yet.

*Say you have the square root of x^2/squarerootof 25-x^2 dx

1. You see what box you need to use (which I need to memorize). There are three different cases: (a is the number, u is the x)
square root of a^2 - u^2 --->asin(t)
square root of a^2 + u^2 --->atan(t)
square root of u^2 - a^2 --->asec(t)
This example would follow a^2 - u^2

2. Then find your x and dx:
x is from the three different cases so x= 5sin(t)
dx is the derivative so dx= 5cos(t)

3. Next you have the square root:
squarerootof 25-x^2 --->5cos(t)
*those are from your chart thing too, but Mal Pal said that it is usually like the opposite of the x

4. and don't forget to account for the x^2:
so take your x, x=5sin(t) and square it which gives you x^2=25sin^2(t)

5. Now plug everything in!
so you should get
25sin^2(t)5cos(t)/5cos(t)
*simplify: the 5cost cancel leaving 25sin^2(t)

Now I'm pretty sure you use the power reduction formulas here right?
But this is where I get stuck..how do I use 1/2 - 1/2cos2x for 25sin^2(t)?

6. I know you integrate after that.

7. form the triangle and use that to plug in to the trig functions
*don't forget SOHCAHTOA