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

Calculus
Tutor: None Selected Time limit: 1 Day

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

Please show all work and a clear answer

Aug 2nd, 2015

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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. 

Please let me know if you nea case for torture by michale levined any clarification. I'm always happy to answer your questions.
Aug 2nd, 2015

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