Question

Find the area of the region bounded by the curve of x=y^2-1 and the y-axis.

Answer 1

how are you going to solve this?

Answer 2

By hand without graphing.

Answer 3

and how are you going to do that exactly?

Answer 4

I don't know, that's why I asked the question.

Answer 5

so you're doing calculus now?

Answer 6

Yes.

Answer 7

what have you learned in the past about area problems?

Answer 8

Take the integral after finding the limits of integration.

Answer 9

okay, go ahead

Answer 10

set up the integral notation

Answer 11

But should the integrand be y^2-1? Or y=sqrt(x+1)?

Answer 12

well does it matter?

Answer 13

would it satisfy the equation if the integral is set up like this?
\[\int\limits (y^2-1) dy \]

Answer 14

I think so. But don't I need to find the limits of integration by setting y^2-1=0 and solve for y?

Answer 15

and I don't know why you mention about limits of integration when the integration problem is indefinite

Answer 16

Are you sure? Because this is about finding the area. The integral must be definite.

Answer 17

so how are you going to find the limits?

Answer 18

from what to what?

Answer 19

That's the part I don't get. If I set y^2-1=0 and solve for y, I get 1 and -1. That means I need to take the integral from -1 to 1. And I was asking you if that's the right way to do it.

Answer 20

okay then set it up that way, but when you do that what happens to your x?

Answer 21

can you make sure first that you've copied down the problem correctly?