Question

How do you find the volume bounded by `y=e^x` and the lines y=0, x=1, x=2 revolved about the y-axis?

Answer 1

Volume`=pi/2(e^4-e^1)`

Explanation:

According to second theorem of Guldino, volume obtined by a rotation of a section bounded by a function `f(x)` and the `x`axis between `a` and `b` is `V=piint_a^bf^2(x)dx`.

In our case, we have `V=piint_1^2e^(2x)dx=pi/2(e^4-e^1)`.