Thank you for the opportunity to help you with your question!

This is a classic case of using integration to find the area between two curves. Our problem already defines the limits of our integral and the variable we are integrating with respect to. We are integrating with respect to x and our limits are from 0 to 1.

In this region y1 is our upper curve and y2 is our lower curve. To find the area between the curves we simply integrate their difference, y1 - y2. This will give us the area from x=0 to x=1, but the problem wants the area of the whole region.

Lucky for us the 2nd enclosed region from x=1 to x=2 is the exact same size as the 1st region, so we can simply multiply our first integral by 2 to get the area of the entire region. We now have all the information necessary to make our integral:

And there is our final answer. Please let me know if you need any clarification. I'm always happy to answer your questions.

Sep 6th, 2015

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