HEYY I NEED HELP WITH AN AP CALC ASSIGNMENT ASAP

CALCULATOR PART

1. The area of R + S is unsigned, meaning you want to find

where is the interval between the leftmost and rightmost intersections of and .

First use your calculator to find these intersections:

so that and . Now compute the integral using your calculator:

2. The volume, using the washer method, is given by the integral

3. A circle of radius has area ; a semicircle with the same radius thus has area . Each cross section of this solid is a semicircle whose diameter is the vertical distance between and , or . In terms of the diameter , the area of each semicircle would be . Then the volume of the solid is

NON-CALCULATOR PART

4. The mean value theorem says that for a function continuous on an interval and differentiable on , there is some such that

If this happens to be an antiderivative of , then we end up with

is continuous and differentiable everywhere, so the MVT applies. We have , so the MVT tells us there is some such that

That is, the average value of on is 0. The MVT says there is some in the interval such that the function takes on the average value itself; this happens for .

5. This question seems to be incomplete...

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