1. The problem statement, all variables and given/known data
Evaluate the iterated integral
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
Let u= 3x+y so that dy= du. When y= 3, u= 3x+3 and when y= 4, u= 3x+4. The integral becomes:
In the first integral, let v= 3x+ 4 so that dx=(1/3)dv. When x= 1, v= 7 and when x= 2, v= 10. That integral becomes
In the second integral, let w= 3x+ 3 so that dx= (1/3)dw. When x= 1, w= 6 and when x= 2, w= 9. That integral becomes .
The original integral is
That is about 0.01626.