Solve Iterated Integral Using Fundamental Theorem & Fubini's

[skaterbasist]

Homework Statement

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

Homework Equations

Fundamental Theorem of Calculus & Fubini's Theorem

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 :(

 

[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 ?

 

[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.