Question

Find the area enclosed by the graphs of the following equations.y=6(x√2−x2)2, y=0, x=1 and x=4

Answer 1

we have the functions

$\begin{gathered} y=6\left(\frac{\sqrt{x}}{2}-\frac{x}{2}\right)^{2} \\ y=0 \end{gathered}$

Interval [1,4]

Using a graphing tool

The area enclosed by the graphs is given by

$\int_1^46\left(\frac{\sqrt{x}}{2}-\frac{x}{2}\right)^2dx=\frac{111}{20}units^2$

The answer is 111/20 units2