Question
Asked Oct 3, 2019
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Use an area formula from geometry to find the value of the integral by interpreting it as the (signed) area under the graph of an appropriately chosen function.

-1010 square root of 100-xdx

type an exact answer, using pi as needed.

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Expert Answer

Step 1

The definite  integral of y with respect to x from x=a to x=b represents the area bounded by y-axis , x-axis x=a and x=b

Step 2

Here y=sqrt(100-x^2) which represents the semicicle above x-axis whose radius is 10. 

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Step 3

So definite integral of sqrt (100-x^2) from x=-10, to x=10 ...

10
100- (10j =
-(10) = 507
2
2
-10
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10 100- (10j = -(10) = 507 2 2 -10

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Math

Calculus

Integration

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