# Area of region of plane between the graph

• Apr 13th 2009, 04:54 PM
Jim Marnell
Area of region of plane between the graph
Find the area of the region of the plane between the graphs of
$\displaystyle y=9-x^2$ and
$\displaystyle y=1+2x$

would $\displaystyle f(x)=9-x^2$
and $\displaystyle g(x)=1+2x$

and then set them equal? $\displaystyle 9-x^2=1+2x$

confused on how to do this problem
• Apr 13th 2009, 05:01 PM
skeeter
Quote:

Originally Posted by Jim Marnell
Find the area of the region of the plane between the graphs of
$\displaystyle y=9-x^2$ and
$\displaystyle y=1+2x$

would $\displaystyle f(x)=9-x^2$
and $\displaystyle g(x)=1+2x$

and then set them equal? $\displaystyle 9-x^2=1+2x$

confused on how to do this problem

$\displaystyle 9-x^2 = 1+2x$

$\displaystyle 0 = x^2+2x-8$

$\displaystyle 0 = (x+4)(x-2)$

intersection points are $\displaystyle x = -4$ and $\displaystyle x = 2$

$\displaystyle A = \int_{-4}^2 (9-x^2) - (1+2x) \, dx$

simplify the integrand, integrate, and use the FTC to find the area.
• Apr 13th 2009, 05:21 PM
Jim Marnell
I'm not sure how to simplify the integrand, probably because im not sure what it means to do that but i can integrate and perform the Fundamental Theorum. Can any1 show me how to simplify the integrand
• Apr 13th 2009, 05:24 PM
skeeter
combine like terms ... that's all.

then integrate.
• Apr 13th 2009, 05:27 PM
Jim Marnell
oh ok thanks again!

so simplified it would just be $\displaystyle -x^2+8+2x$

would area=28?
• Apr 13th 2009, 07:52 PM
mr fantastic
Quote:

Originally Posted by Jim Marnell
oh ok thanks again!

so simplified it would just be $\displaystyle -x^2+8 {\color{red}+} 2x$ Mr F says: No. Please take greater care with your algebra. The red plus is wrong.

would area=28? Mr F says: Given the above mistake, I assume 28 will also be wrong.

The first thing you should have done in this whole question is draw a diagram. Did you do that?
• Apr 14th 2009, 08:21 AM
Jim Marnell
that plus error was my fault, i had it right on paper but typed it in wrong. But yes i had to draw the diagram to go along with the problem but i did it after i completed the problem but definitely would have helped if i drew it before i did the problem