Mathematics

Problem

The region bounded by the lines

x=y

and

x=4-y

for

0\le y\le 2

is revolved about the line

x=1

. a. Identify the value of

y

at which the line

x=1

intersects the region boundary. b. Write the definite integral(s) required to compute the total volume of the resulting solid. c. Evaluate the integral(s) to obtain the exact volume.

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