SOLUTION: Find the area between y = x^3+x^2−20 x and the x-axis.

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Question 972421: Find the area between y = x^3+x^2−20 x and the x-axis.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the points of intersection to define the limits of integration.
Not sure if you need to calculate the entire area so I'll break it up integrating from x=-5 to x=0 and then from x=0 to x=4.
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int%28%28x%5E3%2Bx%5E2-20x%29%2Cdx%29=x%5E4%2F4%2Bx%5E3%2F3-10x%5E2%2BC
So then from x=-5 to x=0, the area A%5B1%5D would be,
A%5B1%5D=%280%5E4-%28-5%29%5E4%29%2F4%2B%280%5E3-%28-5%29%5E3%29%2F3-10%280%5E2-5%5E2%29
A%5B1%5D=%28-625%29%2F4%2B%28125%29%2F3%2B10%2825%29
A%5B1%5D=%28-1875%29%2F12%2B%28500%29%2F12%2B3000%2F12
A%5B1%5D=1625%2F12
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And the area A%5B2%5D from x=0 to x=4 would be,
A%5B2%5D=%284%5E4-%280%29%5E4%29%2F4%2B%284%5E3-%280%29%5E3%29%2F3-10%284%5E2-0%5E2%29
A%5B2%5D=64%2B64%2F3-160
A%5B2%5D=192%2F3%2B64%2F3-480%2F3
A%5B2%5D=-224%2F3
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So the entire area would be,
A=A%5B1%5D%2BA%5B2%5D
A=1625%2F12-224%2F3
A=1625%2F12-896%2F12
A=729%2F12
highlight%28A=243%2F4%29