The functions f(x)=2-x^2 and g(x)=-x are given
a)Find the area of the region bounded by the graphs of f(x) and g(x).
b)Find the area of the region bounded by the graph of f(x) and the x-axis.

Question

The functions f(x)=2-x^2 and g(x)=-x are given
a)Find the area of the region bounded by the graphs of f(x) and g(x).
b)Find the area of the region bounded by the graph of f(x) and the x-axis.

serenity74 · Answer

So in order to find the bounds you HAVE to equal the two graphs together and you get the bounds...Do you know how to do that?

anonymous · Answer

Ya I set them equal to each other since both functions equal y, solve for x and those values are my bounds. For part a I got -1,2 and for part b, -sqrt2 sqrt2.

serenity74 · Answer

Good. Now lets focus on part a okay?
Part a you look for a number between -1 & 2 and then plug it in to the FUCTIONS and see which one is "bigger" so you can determine which graph is the top graph and which graph is the bottom graph.

anonymous · Answer

the top graph would be 2-x^2 and the bottom graph would be -x

serenity74 · Answer

Sorry got sidetracked!

anonymous · Answer

from that point, I would do the integral from -1 to 2 of 2-x^2-x dx --> which would then equal 11/6

anonymous · Answer

all good man

serenity74 · Answer

Indeed

serenity74 · Answer

You practically do the same thing for part B lol. Instead of the dy in the integral form you put dx since it's asking for X-axis

anonymous · Answer

my answer is 2sqrt2 - 4/3?

serenity74 · Answer

That's what I got....

anonymous · Answer

alright cool, thanks for the help!

serenity74 · Answer

:) If the second one is wrong...I am sorry I am so tired lol. I am still working on the stupid cross sections lol.