Iterated Integral

[CatchThis2]

This is one of my homework problems which is due in a few hours which I have been unable to get. Could someone show me how to get the answer. Greatly appreciate the help!

 

[daon]

\(\displaystyle u = 2x+y, du=1dy\)

\(\displaystyle \int_3^4 (2x+y)^{-2} dy = -u^{-1} = -(2x+y)^{-1} |^{^{y=4}}_{_{y=3}} = \frac{1}{(2x+3)(2x+4)}\)

For the outer integral, simply use a partial fraction decomposition. It will have two natural log answers.

 

[daon]

Oh lawd. I combined the fractions and told you to uncombine them. Just work with what you get from plugging in 3 and 4. Running on 3 hrs of sleep here :roll: