What isthe area bounded by and from $x = \frac{π}{4}$ $x=pi/4$ to $x = \frac{5 π}{4}$ $x=(5pi)/4$ ?

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What isthe area bounded by and from $x = \frac{π}{4}$ $x=pi/4$ to $x = \frac{5 π}{4}$ $x=(5pi)/4$ ?

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

1 Answer

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Answer 1 · 2018-05-23T04:54:34

$A = A_{p u r p} + A_{r e d} = 1 - 0.293 = 0.707$ $A=A_(purp)+A_(red)=1-0.293=0.707$

Explanation:

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

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

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

![desmos.com]( useruploads.socratic.org )

now let calculate the area:

$A = A_{p u r p} + A_{r e d}$ $A=A_(purp)+A_(red)$

$A_{p u r p} = \int_{\frac{π}{4}}^{π} sin x \cdot d x = {[- cos x]}_{\frac{π}{4}}^{π}$ $color(purple)[A_(purp)=int_(pi/4)^pisinx*dx=[-cosx]_(pi/4)^pi]$

$= - cos π + cos (\frac{π}{4}) = 1 + 0 = 1$ $color(purple)[=-cospi+cos(pi/4)=1+0=1]$

$A_{r e d} = \int_{π}^{5 \frac{π}{4}} - sin x \cdot d x = {[cos x]}_{π}^{5 \frac{π}{4}}$ $color(red)[A_(red)=int_pi^(5pi/4)-sinx*dx=[cosx]_pi^(5pi/4)]$

$= cos π - cos (5 \frac{π}{4}) = - 1 + \frac{1}{\sqrt{2}} = 0.707 - 1 = - 0.293$ $color(red)[=cospi-cos(5pi/4)=-1+1/sqrt2=0.707-1=-0.293]$

$A = A_{p u r p} + A_{r e d} = 1 - 0.293 = 0.707$ $A=A_(purp)+A_(red)=1-0.293=0.707$

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What isthe area bounded by and from $x = \frac{π}{4}$ $x=pi/4$ to $x = \frac{5 π}{4}$ $x=(5pi)/4$ ?

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

1 Answer

Explanation:

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What isthe area bounded by and from x=π4x=pi/4 to x=5π4x=(5pi)/4?

A)Find the area bounded by and from x=π4x=pi/4 to x=5π4x=(5pi)/4 Make an accurate sketch of the graphs on the axes.

1 Answer

Explanation:

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Impact of this question

What isthe area bounded by and from $x = \frac{π}{4}$ $x=pi/4$ to $x = \frac{5 π}{4}$ $x=(5pi)/4$ ?

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