Integral problem, I'll post a picture of it. Please help :)

Question

dumbcow · Answer

the link goes to your login page

anonymous · Answer

$$f(x)=x^3-9x^2+33x+2$$

anonymous · Answer

$$\int\limits_{1}^{2}f(x)dx$$

anonymous · Answer

$$\int\limits_{27}^{40}f ^{-1}(x)dx$$

anonymous · Answer

I'm supposed to find a relation between those two integrals by drawing a suitable picture, and then use that to figure out the answer for the 27-40 integral.

anonymous · Answer

Sorry, I should word that a little better. I don't use the picture to find the answer. I draw the picture to find the relationship, and then use that relationship to find the answer for the 27-40 integral

dumbcow · Answer

notice f(2) = 40 and f(1) = 27
thus
f^-1 (40) = 2  and f^-1 (27) = 1

so the area of each region is the same

anonymous · Answer

Okay. When I solved the first interval I got 27. So the area should also be 27 for the second one is what you're saying?

dumbcow · Answer

hmm its not 27...check your integration

anonymous · Answer

Okay. See, we're stuck doing it the long way because my professor wants us to use the Riemann sums to integrate for now. I'll try it again. Thanks for the help! :)

anonymous · Answer

You don't have to stick around if you don't want, I'll probably get it right this time. It might take me a couple more minutes so I don't want to waste your time.

dumbcow · Answer

no prob...ok i didn't know you were using Riemann sums
27 is ok for left hand sum i guess