Question

How do I find the area of the region bound by
y= -x^2 +3x and y=0? Help appreciated!!

Answer 1

I am learning about integration right now in Calculus, so I don't think it is supposed to be solved with rectangles and estimation... or is it?
Is there some way I should be using integration to find the answer?

Answer 2

if you want the exact answer you need to use the integral. Rectangles can only approximate.

Answer 3

Ok, I think since we have already covered estimation with rectangles, integration is what my teacher is looking for.

Answer 4

So the shaded area created by these graphs would go from (0,0) to (3,0)
so would I set up an integral like this?
\[\int\limits_{0}^{3} -x^2 +3x\]

Answer 5

exactly
don't forget to write the differential, dx, at the end of the integral to show you are integrating with respect to x. It may seem unimportant now, but it's a good habit to develop

Answer 6

Right, I forgot to put dx.
So I will just integrate -x^2 +3x with respect to x on the interval [0,3] and the answer is the area?
I had thought it would be more difficult with two equations, but I suppose y=0 is a simple one so they gave me a break. :)

Answer 7

yep, with y=0 it makes it pretty straightforward. Don't worry, I'm sure you'll have some tougher ones down the road.

Answer 8

I got 9/2 , or 4.5, for my answer. Thank you for the help, I have two more problems like this. I think I solved one with integration and the other with rectangles. So I'm going to go re-do the rectangle one now that I know what they're asking for. Anyway, here's a medal!

Answer 9

Cool, happy to help
good luck!