# Integral of a sqrt of polynomial

1. Mar 23, 2009

### ldbaseball16

1. The problem statement, all variables and given/known data
(1/sqrt(x^2+16), x, 0, 4);

2. Relevant equations
x=4tan(theta)
dx=4sec^2(theta)d(theta)

3. The attempt at a solution
(1/sqrt(16+(4tan(theta))^2)(4sec^2theta) Im confused can i get some help??

2. Mar 23, 2009

### AEM

Re: Intergrals

If you remember that

$$1 + tan^2 \theta = sec^2 \theta$$

then you'll find that the integrand simplifies quite nicely. Don't forget to change your integration limits appropriately.

3. Mar 23, 2009

### ldbaseball16

Re: Intergrals

ok, i got ln(4/sqrt(x^2 +16) + (x/4)???? is this right??????

4. Mar 23, 2009

### lanedance

Re: Intergrals

hmmm.... if this is a definite you don't need to try and convert back to x's, just change the integration limits when you make the variable change

5. Mar 24, 2009

### AEM

Re: Intergrals

I think that's pretty close. As the previous post mentions, I didn't change back to the x's but worked with theta limits of 0 to pi/4.

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