Question

The region under the graph of y=3^(-x) from x=1 to x=2 is revolved about the x-axis. Find the volume of the resulting solid.

Answer 1

you have to find the definite integral using the formula V = \[\int\limits_{a}^{b} \pi(f(x))^2 \] so the first step is you have to square y=3^-x. since x = 1 and x = 2, the limits of the definite integral will be a = 1, to b = 2. you can take the pi out becuase its a constant and add it back in later. do you kind of get it? you have to imagine like cylinder like shape and imagine chopping it up into little slices

Answer 2

Sweet, thank you for the in-depth answer. How did you know to use the Washer/Disc method instead of using the Cylinder method?

Answer 3

When you slice it up in x, and spin around in the y direction (as pictured here), you get disks.