Find the area enclosed by the graphs of each of the following y=x+1,line x=-2, x=2 and y=x²-1 ?

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Answer 1 · 2018-05-30T20:56:00

#A=int_2^-1x^2 - 1-(x+1)dx = 9/2#

The only equations that matter are:

#y=x^2 - 1#

#y=x+1#

First determine where these intersect:

#x^2 - 1 =x+1#

#x^2 - x -2=0#

#(x+1)(x-2)=0#

#x= 2#
#x=-1#

#A=int_2^-1x^2 - 1-(x+1)dx#

#A=int_2^-1x^2 - 1-x-1dx#

#A=int_2^-1x^2 -x-2dx#