The graph of g consists of two straight lines and a semicircle. Use it to eveluate the integral.12210203861.jpgint_10^30 g(x)dx

Albarellak 2021-02-05 Answered

The graph of g consists of two straight lines and a semicircle. Use it to eveluate the integral.
image
1030g(x)dx

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Expert Answer

Aniqa O'Neill
Answered 2021-02-06 Author has 100 answers

The integral 1030g(x)dx is the area between the graph of g and the horizontal x-axis on the interval 10x30.
We note that this area forms a semicircle with radius r = 10. Since the semicricle lies below the horizontal axis, the integral will be negative.
The area of a circle is the product of π and the squared radius r2. The area of a semicircle is half the area of a circle.
1030g(x)dx=πr22
=π(102)2
=100π2
=50π
157.0796

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