Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region bounded by y  1 3 ex2 /3 , y  0, x  0, and x  3 about the y-axis. Round your answer to three decimal places.

Step-by-step explanation:

y = 0, x = 0 and x = 3

Consider an element of thickness dx at a distance x from the origin. By Cylindirical Shell Method, the volume of the element is given by

Integrate the above integral over the limits x=0 to x=3 which implies

Solve by subsititution

Also, apply the new limits

This implies,

Let,

Integrate by parts the above integral

Integrate by parts formula

Again integrate by parts

Integrate by parts formula

Therefore,

This implies, the volume is

That is, up to three decimal places

your answer is a

step-by-step explanation:

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step-by-step explanation: