Proof using the Fundamental Theorem of Calculus

• February 14th 2011, 05:54 AM
zebra2147
Proof using the Fundamental Theorem of Calculus
Im supposed to prove the following by using the Fundamental Theorem of Calculus twice...

$\int_{c}^{d}(\int_{a}^{b}\rho _{x}(x,y)dx)dy=...=\int_{a}^{b}(\int_{c}^{d}\rho _{x}(x,y)dy)dx$.

Along with the Fundamental Theorem of Calculus I also think that Fubini's Theorem might play a role in this proof...

I'm just not sure how to get the ball rolling. Any help would be appreciated.
• February 14th 2011, 06:41 AM
xxp9
but this is part of the Fubini's theorem
• February 14th 2011, 06:50 AM
zebra2147
Right...I guess I was just stating that although it is a part of Fubinin's Theorem we are asked to use the Fundamental Theorem of Calculus to show that it works.