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

$A = \int_{2}^{- 1} x^{2} - 1 - (x + 1) d x = \frac{9}{2}$ $A=int_2^-1x^2 - 1-(x+1)dx = 9/2$

The only equations that matter are:

$y = x^{2} - 1$ $y=x^2 - 1$

$y = x + 1$ $y=x+1$

First determine where these intersect:

$x^{2} - 1 = x + 1$ $x^2 - 1 =x+1$

$x^{2} - x - 2 = 0$ $x^2 - x -2=0$

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

$x = 2$ $x= 2$
$x = - 1$ $x=-1$

$A = \int_{2}^{- 1} x^{2} - 1 - (x + 1) d x$ $A=int_2^-1x^2 - 1-(x+1)dx$

$A = \int_{2}^{- 1} x^{2} - 1 - x - 1 d x$ $A=int_2^-1x^2 - 1-x-1dx$

$A = \int_{2}^{- 1} x^{2} - x - 2 d x$ $A=int_2^-1x^2 -x-2dx$