Question

Asked Jan 22, 2020

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Find the volume of the solid generated by re-volving the region in the first quadrant bounded by the coordinate axes, the curve y = e-x, and the line x = 1

a. about the y-axis.

b. about the line x = 1.

Step 1

We need to find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^{-x}, and the line x = 1.

- about the y-axis.

So, the graphical representation looks like the following where the intersection point of the curve y = e^{-x}, and the line x = 1 is also shown.

Step 2

So, the volume is given by,

Step 3

Now,

- about the line x = 1.

So, the graphical representation looks like the following where the intersection ...

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