In the inequality, what are all the possible values of x?
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Answer:
The volume is:
Step-by-step explanation:
See the sketch of the region in the attached graph.
We set the integral using washer method:
Notice here the radius of the washer is the difference of the given curves:
So the integral becomes:
We solve it:
Factor out and distribute the exponent (you can use FOIL):
Notice:
So the integral becomes:
Then using the basic rule to evaluate the integral:
Simplifying a bit:
Then plugging the limits of the integral:
Taking the root (rational exponents):
Then doing those arithmetic computations we get:
