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:

$x^2 - 1 =x+1$

$x^2 - x -2=0$

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

$x= 2$
$x=-1$

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

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

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