Find the area of the region bounded by f(y) and g(y):
f(y)=y^2 - 1
g(y)=4-(y-1)^2

Question

Find the area of the region bounded by f(y) and g(y):
f(y)=y^2 - 1
g(y)=4-(y-1)^2

amistre64 · Answer

whats our points of intersection?

anonymous · Answer

Well, we need to set them equal to find them, right?
Well, I don't really know how to get the exact numbers. I used the calculator and got:
(.381966,-.618034) and (2.618034,1.618034)

anonymous · Answer

|dw:1332453432738:dw|
Looks something like that

amistre64 · Answer

y^2 - 1 =  4-(y-1)^2

y^2 - 1 =  4-(y^2-2y+1)

y^2 - 1 =  4-y^2+2y-1

2y^2-2y  = 4

y^2-y +1/4= 2+1/4

y = 1/2 +- 3/2

sound about right?

amistre64 · Answer

y=2,-1

amistre64 · Answer

so,$$\int_{-1}^{2}f(y)-g(y)\ dy$$
and if you get a negative result ignore the sign.

anonymous · Answer

Alright, I got 9, is that the correct answer?

amistre64 · Answer

dunno, i got know idea if you did the integrations right

amistre64 · Answer

they are pretty basic tho so im sure they aint that hard to mess up :)

anonymous · Answer

yup lol thanks =)