# Integeral: Trig Substitution help

• Feb 23rd 2009, 05:13 PM
squeeze
Integeral: Trig Substitution help
http://www.sitmo.com/gg/latex/latex2...7D%7D%7Bx%7Ddx

I have this equation

So I refer to a triangle and use these values for substitution.

http://www.codecogs.com/eq.latex?%5C...x%5E%7B2%7D%7D = 5 cos(x)

x = 5 sin(x)

dx = 5 sin(x) = 5 cos(x)

I ended up having something like this.

http://www.sitmo.com/gg/latex/latex2...Csin%28x%29%7D

I canceled the 5 sin(x)s leaving me with

integral(5 cos x) = - 5 sin x + c

I looked at the triangles and got back.

x/5 + c

Then I looked back at the book for answers and I was way way way off.

What did I do that was totally wrong?
• Feb 23rd 2009, 05:34 PM
mpl06c
hey man i dont think u set up your triangle properly.. it should be (25-x^2)^1/2 divided by 5
• Feb 23rd 2009, 05:42 PM
squeeze
http://emweb.unl.edu/math/mathweb/trigonom/Image289.gif

a = sqrt(25-x^2)
b = x
c = 5

^ I thought that is how you normally set it up for a sqrt(c^2 - x^2) situation where c is a constant.
• Feb 23rd 2009, 07:09 PM
mpl06c
No that's wrong. You solved for it. Cos=x/5 so adjacent is x and 5 is the hypotnuse using pythagorems theorm you can solve for the other side