# Integral of a sqrt of polynomial

#### ldbaseball16

1. Homework Statement
(1/sqrt(x^2+16), x, 0, 4);

2. Homework 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??

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#### AEM

Gold Member
Re: Intergrals

1. Homework Statement
(1/sqrt(x^2+16), x, 0, 4);

2. Homework 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??
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.

#### ldbaseball16

Re: Intergrals

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

#### lanedance

Homework Helper
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

#### AEM

Gold Member
Re: Intergrals

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