What is the Solution to a Challenging Integration Homework Problem?

[MillerL7]

I attached just one question...My tutor and the TA could not figure it out or help me get started on it...can someone help me get started? Thank you so much!

 

[HallsofIvy]

First Please type the problem in rather that posting a "word" file. It's not that difficult and many people won't open a "word" attachement for fear of viruses. I wouldn't if I didn't have very strong virus protection.

As for the problem itself, Draw a picture. While you don't know the exact "form" of f, you know that it passes through the points (5, 13) and (11, 6) and is decreasing so you can sketch a possible graph for f. You also know that the integral given is the area under that curve- the area between that curve and the x-axis. Draw the boundaries of that region.

Now, f^-1 just "swaps" x and y so the integral of f^-1 you are looking for is the area between that curve and the y- axis. Draw the boundaries and conpare the two areas.