# Solutions to Problem Set 10

Math 211-03

9-25-2017

[Area]

1. Find the area of the region between and from to .

The curves do not intersect on the interval .

The top curve is and the bottom curve is . The area is

2. Find the area of the region between and from to .

The curves do not intersect on the interval . Using vertical rectangles, I get the following integral for the area:

3. Find the area of the region bounded by the curves and .

Set the curves equal to find the intersection points:

Using vertical rectangles, I get the following integral for the area:

4. Find the area of the region bounded by the curves and .

Find the intersection points:

The curves intersect at and at . Since is a parabola opening downward and is a parabola opening upward, is the top curve and is the bottom curve. The area is

5. Find the area of the region under and above the x-axis, from to .

The area is given by the following improper integral:

Do not wish to be anything but what you are. - Saint Francis de Sales

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