### Home > APCALC > Chapter 4 > Lesson 4.2.3 > Problem4-75

4-75.

Given $f\left(x\right) = 2x$, write the equation of a vertical line that will divide $\int_0^{10}f\left(x\right)dx$ in half.

Sketch a graph of

$\int_{0}^{10}2xdx$

Find the area under the graph from $[0, 10]$ through integration.

$\int_{0}^{10}2xdx=x^{2}\left|\begin{matrix} 10\\ 0 \end{matrix}\right.=100$

Because you want to find the equation that would divide the area of the graph in half, you must solve the following equation:

$x^{2}\left|\begin{matrix} x\\ 0 \end{matrix}\right.=50$

$x^{2}= 50$

$x=\sqrt{50}=5\sqrt{2}$

Use the eTool below to examine the graph.
Click the link at right for the full version of the eTool: Calc 4-75 HW eTool