Calculating Area Between Two Curves

[Peter G.]

Find the area of the region bounded by the following curves:

y=x²-5x and y=3-x²

Answer:

So, using simultaneous equations I found the points of intersection (x = -0.5 and x = 3). The book agrees with me on that.

I then performed the following:

3-x²-(x²-5x)

= -2x²+5x+3

I then integrated that:

((-2/3)*x³)+((5/2)*x²)+3x

I then subtracted the result when I substitute -0.5 from the result I get when I substitute 3. The book claims the answer is 2.655 but, no matter how hard I try I keep getting (271/24)

Can anyone help me here please?

Thanks!

 

[LCKurtz]

The work you showed so far is correct. Unfortunately I get 343/24 = 14.29 which doesn't agree with either of yours. Your book's answer is obviously wrong; clearly too small for the area enclosed.

 

[Peter G.]

Hi! Thanks a lot for your response. I must be making some calculation error! When I try using the graphic calculator to find the integral it gives me 14.29, so, yeah, you should be right. I will try again.

Thanks once again,
Peter