SOLUTION: Use the definite integral to find the area between the​ x-axis and​ f(x) over the indicated interval. Check first to see if the graph crosses the​ x-axis in the g

Algebra ->  Trigonometry-basics -> SOLUTION: Use the definite integral to find the area between the​ x-axis and​ f(x) over the indicated interval. Check first to see if the graph crosses the​ x-axis in the g      Log On


   

Question 1032445: Use the definite integral to find the area between the​ x-axis and​ f(x) over the indicated interval. Check first to see if the graph crosses the​ x-axis in the given interval.
f(x)=1-x^2; [0,2]
Question: The area between the x-axis and f(x) is ???
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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A=int%28%28f%28x%29%29%2Cdx%2C0%2C1%29%2Bint%28%28-f%28x%29%29%2Cdx%2C1%2C2%29
A=int%28%281-x%5E2%29%2Cdx%2C0%2C1%29%2Bint%28%28x%5E2-1%29%2Cdx%2C1%2C2%29
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A%5B1%5D=x-x%5E3%2F3%2BC
A%5B1%5D=%281-0%29-%281%5E3-0%5E3%29%2F3
A%5B1%5D=1-1%2F3
A%5B1%5D=2%2F3
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A%5B2%5D=x%5E3%2F3-x%2BC
A%5B2%5D=%282%5E3-1%5E3%29%2F3-%282-1%29
A%5B2%5D=%288-1%29%2F3-1
A%5B2%5D=7%2F3-3%2F3
A%5B2%5D=4%2F3
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A=A%5B1%5D%2BA%5B2%5D
A=2%2F3%2B4%2F3
A=2
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This previous method assumes the area below the x-axis is treated as positive also.
If you treat this as negative then the sum would change to,
A=A%5B1%5D-A%5B2%5D
A=2%2F3-4%2F3
A=-2%2F3