25. any1 know calculus?

Question

the region enclosed by the graphs of y=e^(x/2) , y=1, and x=ln3 is revolved about the x-axis find the volume of the solid generated

Answer 1

if you plot the functions or set them equal to each other you'll notice that the two Y functions intersect with each other at x = 0 and with the x function at x = ln(3)

so you'll want to integrate e^(x/2) from 0 to ln(3) and then subtract from that the integral of 1 from 0 to ln(3). that will give you the somewhat triangular area that those three functions bound.

Now that you have the cross section you can integrate that area from 0 to 2*pi and you should have the volume.

Answer 2

y=1 corresponds to x=0
so you must calculate the integral
Intpi y^2dx between 0 and ln3=
Intpi e^x dx (o,ln3) = 2pi

Answer 3

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