1. Using washers, the volume is given by the integral


We're using washers whose centers depend on the value of
, hence we integrate with respect to
2. The area of the given region is given by the integral

To compute the integral, first consider the substitution
, or
so that
. Then
and
, so the integral is equivalently

Integrate by parts, taking


so that

and
, so the area is

For the remaining integral, substitute
, so that
. Then
and
:

(notice that the integral is improper)


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Answer:
Choose a point on the graph to find the value of the derivative at. Draw a straight line tangent to the curve of the graph at this point. Take the slope of this line to find the value of the derivative at your chosen point on the graph.
Explanation:
The derivative measures the steepness of the graph of a function at some particular point on the graph. Thus, the derivative is a slope.
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