What are the limits for these integration problems?

[BuBbLeS01]

Homework Statement

A. (1-sin^2x)/(cos^2x) dx
Upper Limit = pi/4
Lower Limit = 0

B. (x-2)/(sqrt x) dx
Upper Limit = 4
Lower Limit = 1

Homework Equations

The Attempt at a Solution

A. I am having trouble with this one.
B. (x - 2)/(x^1/2) = (x^1/2 - 2x^-1/2) =
2/3x^3/2 - 4x^1/2

I plug in 4 and 1 and I get 2/3

 

[hotcommodity]

For part a, think about the identity $$sin^2x + cos^2x = 1$$

 

[BuBbLeS01]

Oh I KNEW it! That was the only thing I could come up with but I wasn't sure if I could do that.

(1-sin^2x)/(cos^2x) dx

ummm so I get...

(cos^2x)/(cos^2x) dx = 1 dx = x??

 

[hotcommodity]

That's correct, now just plug in the limits. For part b think about breaking up the one fraction into two fractions, each with the same denominator, then you can use the power rule for integrating.

 

[BuBbLeS01]

A. = pi/4
B. Do you mean like simplify it? If so then our teacher doesn't want us to simplify at all. If not I don't understand what you mean.

 

[hotcommodity]

Ok nevermind, I didn't see that you had already solved it in your first post. It's correct.

 

[BuBbLeS01]

Ok nevermind, I didn't see that you had already solved it in your first post. It's correct.

Oh okay...well thank you so much for your help! I have a big test on Monday so I am sure I will be on later but I am too tired right now hehe. Thanks again!

 

[hotcommodity]

You're quite welcome, good luck on your test :)