Consider the region enclosed by the curves y= 12-x^2 and y= x^2-6.

a. Sketch the region enclosed by the curves. Label the intersection points with their coordinates.

b. Decide whether to integrate with respect to x or y then find the area of the region.

Question

Consider the region enclosed by the curves y= 12-x^2 and y= x^2-6.

a. Sketch the region enclosed by the curves. Label the intersection points with their coordinates. 

b. Decide whether to integrate with respect to x or y then find the area of the region.

anonymous · Answer

Do you own a graphing calculator? the enclosed region can be viewed and the integration with respect to the x or y axis will become lucid after you examine the graph and use the formula for the area between curves.

anonymous · Answer

Got it, thank you tho !

john_es · Answer

If you don't have a graphic calculator, you can use the web, https://www.wolframalpha.com/input/?i=Plot++y%3D+12-x%5E2+and+y%3D+x%5E2-6

anonymous · Answer

Instead of using graphic calculator, try to use your imagination first. Notice that bouth equations are simple parábolas. One is opened upwords( plus sign in front of $x^2$) and other opend downwords (minus sign in front of $x^2$). The vertexes are at (0,12) and (0,-6). Now try to draw this:
|dw:1399287327641:dw|
So you got all you need to answer the second part of the question without any calculator