Integral of a sqrt of polynomial

[ldbaseball16]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

(1/sqrt(16+(4tan(theta))^2)(4sec^2theta) I am confused can i get some help??

 

[AEM]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

(1/sqrt(16+(4tan(theta))^2)(4sec^2theta) I am 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]

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

 

[lanedance]

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]

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.