The question says: "let A(t) be the area of the region in the first quadrant enclosed by the coordinate axes, the curve y=e^-x and the line x=t>0. Let V(t) be the vlume of the solid generated by revolving the region about the x-axis. Find the following limits: lim t-> infinity A(t), lim t-> infinity V(t)/A(t)."
Okay, so the first thing I did was integrate e^-x from 0 to t. The antiderivative of e^-x is -e^-x. Would that be A(t)? Because, when I took the limit as t->infinity, the value of -e^-x would get closer to 0. But the answer in the back of my book says 1.
Similarly, I used the disc method and then integrated the function pi(e^-x)^2 from 0 to t. I got: -2pi(e^-2x). However, I didn't try to take the limit of this because I had gotten the previous one wrong. Where is my mistake in all of this?