# Iterated Integrals

1. Jun 27, 2010

### skaterbasist

1. The problem statement, all variables and given/known data

Evaluate the iterated integral [URL]https://webwork.csun.edu/webwork2_files/tmp/equations/e4/1efafbd0e820388c5c73acc695601b1.png[/URL]

2. Relevant equations

Fundamental Theorem of Calculus & Fubini's Theorem

3. The attempt at a solution

I have been working on this problem for the last hour and haven't been able to solve it thus far. I integrated the inside of the integral with respect to y from 4 to 3, and then integrated the result from the first integral with respect to x from 2 to 1. In the process, I used substitution to solve the integrals.

The answer I keep on getting is ($$1/(4(3x+4)^4)$$) - ($$1/(4(3x+3)^4)$$) and solve from x= 2 to 1 which results in a small fractional answer of 7.5674005*10^(-5). But my online program keeps on saying its incorrect.

Can anyone give me a heads up as to where I am going wrong? This is one of the few iterated integrals that is giving me problems right now :(

Last edited by a moderator: Apr 25, 2017
2. Jun 27, 2010

### System

Its better to post your work.
Here is a start:
the integration of 1/(3x+y)^2 with respect to y from y=3 to y=4 is :
(-1/3x+4) - (1/3x+3)
and this result is easy to integrate with repsect to x, isn't it ?

3. Jun 27, 2010

### skaterbasist

I found out what my problem was. I made the stupid mistake of differentiating u^-2 when I should have integrated. Thank you. Your first integration was correct, and that was what was causing my mistake.