# Urgent in need of help! Find the area between the curves

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Find the area between the curves y=x+2 and y=x^2-4

Aug 2nd, 2015

To find the points of intersection of the curves, we solve the equations of the curves simultaneously.
Therefore
x^2 - 4 = 2x - x^2
x^2 - 4 - 2x + x^2 = 0
2x^2 - 2x - 4 = 0
Divide by 2
x^2 - x - 2 = 0
(x+1)(x-2) = 0
x = -1, 2

The area A = |integral (x^2 - 4) - (2x - x^2) dx from -1 to 2|
= |integral x^2 - 4 - 2x + x^2 dx from -1 to 2|
= |integral 2x^2 - 2x - 4 dx from -1 to 2|
= | 2x^3/3 - 2x^2/2 - 4x from -1 to 2 |
= | 2x^3/3 - x^2 - 4x from -1 to 2 |
= | (2 * 2^3/3 - 2^2 - 4*2) - [2*(-1)^3/3 - (-1)^2 - 4(-1)] |
= |(16/3 - 4 - 8) - (-2/3 - 1 + 4)|
= |16/3 - 12 + 2/3 + 1 - 4|
= |16/3 + 2/3 - 12 + 1 - 4|
= |18/3 - 15|
= |6 - 15|
= |-9|
= 9
Ans: 9
Note: | | stands for absolute value.

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Aug 2nd, 2015

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Aug 2nd, 2015
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Aug 2nd, 2015
Nov 24th, 2017
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