Find the area of the region bounded by the curves?

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Find the area of the region bounded by the curves?

$y = 2 sin x$ $y=2\sinx$ , $y = 2 cos x$ $y=2\cosx$ , $x = 0$ $x=0$ , and $x = \frac{π}{2}$ $x=\pi/2$

1 Answer

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Answer 1 · 2018-06-02T07:46:54

$4 - \sqrt{2}$ $4-sqrt(2)$

Explanation:

Solving the equation

$2 sin (x) = 2 \cdot cos (x)$ $2sin(x)=2*cos(x)$
in the given interval
we get

$x = \frac{π}{4}$ $x=pi/4$
So our area can be calcultated as

$A = 2 \int_{0}^{\frac{π}{4}} sin (x) d x + 2 \int_{\frac{π}{4}}^{\frac{π}{2}} cos (x) d x$ $A=2int_0^(pi/4)sin(x)dx+2int_(pi/4)^(pi/2)cos(x)dx$
this gives
$A = 4 - 2 \sqrt{2}$ $A=4-2sqrt(2)$

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Find the area of the region bounded by the curves?

$y = 2 sin x$ $y=2\sinx$ , $y = 2 cos x$ $y=2\cosx$ , $x = 0$ $x=0$ , and $x = \frac{π}{2}$ $x=\pi/2$

1 Answer

Explanation:

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Find the area of the region bounded by the curves?

y=2\sinxy=2sinxy=2\sinx, y=2\cosxy=2cosxy=2\cosx, x=0x=0x=0, and x=\pi/2x=π2x=\pi/2

1 Answer

Explanation:

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$y = 2 sin x$ $y=2\sinx$ , $y = 2 cos x$ $y=2\cosx$ , $x = 0$ $x=0$ , and $x = \frac{π}{2}$ $x=\pi/2$