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

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