How do you find the area between #f(y)=y^2, g(y)=y+2#?

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Answer 1 · 2017-01-04T12:39:37

#S=9/2#

The intercept points between the two curves can be found from:

#y^2=y+2#
#y^2-y-2=0#
#y=frac (1+-sqrt(1+8)) 2=(1+-3)/2#

So #y_1=-1# and #y_2=2#

In the interval between the roots we have:

#y^2-y-2<0#

#y^2 < y+2#

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so the are between the curves is calculated as:

#S= int_(-1)^2 (y+2- y^2)dy = [y^2/2+2y-y^3/3]_(-1)^2=2+4-8/3-1/2+2-1/3 = 9/2#