Find the volume V of the solid obtained by rotating the region enclosed by the graphs

Question

Find the volume V of the solid obtained by rotating the region enclosed by the graphs of y = e^−x, y = 1 − e^−x, and x = 0 about y = 2.5.

Answer 1

Be sure to pause the video and work out the details as suggested.

Here is the url to the Desmos graph referenced in the video,

https://www.desmos.com/calculator/jlyfxkxm7p

Answer 2

integrate using the disc method. the disc will be vertical in this case with the variable of integration in the x direction.

r(outside) = 2.5-(1-exp(-x)) = 1.5+exp(-x)

r(inside) = 2.5-exp(-x)

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