Question

The graph of g consists of two straight lines and a semicircle. Use it to eveluate the integral. 12210203861.jpg int_0^10 g(x)dx

Applications of integrals
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asked 2021-02-01
The graph of g consists of two straight lines and a semicircle. Use it to eveluate the integral.
image
\(\displaystyle{\int_{{0}}^{{10}}}{g{{\left({x}\right)}}}{\left.{d}{x}\right.}\)

Answers (1)

2021-02-02
The integral \(\displaystyle{\int_{{0}}^{{10}}}{g{{\left({x}\right)}}}{\left.{d}{x}\right.}\) is the area between the graph of g and the horizontal x-axis on the interval \(\displaystyle{0}\le{x}\le{10}\).
We note that this are forms a triangle with base b = 10 and height h = 20.
The area of a triangle is the product of the base b and the height h, divided by 2.
\(\displaystyle{\int_{{0}}^{{10}}}{g{{\left({x}\right)}}}{\left.{d}{x}\right.}=\frac{{{b}\cdot{h}}}{{2}}\)
\(\displaystyle=\frac{{{10}\cdot{20}}}{{2}}\)
\(\displaystyle=\frac{{200}}{{2}}\)
=100
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