# What isthe area bounded by and from x=pi/4 to x=(5pi)/4?

## A)Find the area bounded by and from $x = \frac{\pi}{4}$ to $x = \frac{5 \pi}{4}$ Make an accurate sketch of the graphs on the axes.

May 23, 2018

$A = {A}_{p u r p} + {A}_{red} = 1 - 0.293 = 0.707$

#### Explanation:

If your question was find the area bounded by and from $x = \frac{\pi}{4}$ to $x = \frac{5 \pi}{4}$ .

i think here you must suppose the function
like bounded by $y = \sin x$

show below the wanted area (shaded) in the graph.

now let calculate the area:

$A = {A}_{p u r p} + {A}_{red}$

$\textcolor{p u r p \le}{{A}_{p u r p} = {\int}_{\frac{\pi}{4}}^{\pi} \sin x \cdot \mathrm{dx} = {\left[- \cos x\right]}_{\frac{\pi}{4}}^{\pi}}$

$\textcolor{p u r p \le}{= - \cos \pi + \cos \left(\frac{\pi}{4}\right) = 1 + 0 = 1}$

$\textcolor{red}{{A}_{red} = {\int}_{\pi}^{5 \frac{\pi}{4}} - \sin x \cdot \mathrm{dx} = {\left[\cos x\right]}_{\pi}^{5 \frac{\pi}{4}}}$

$\textcolor{red}{= \cos \pi - \cos \left(5 \frac{\pi}{4}\right) = - 1 + \frac{1}{\sqrt{2}} = 0.707 - 1 = - 0.293}$

$A = {A}_{p u r p} + {A}_{red} = 1 - 0.293 = 0.707$