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y-sin-x-2-y-x-2-pi-pi-x-pi-Find-the-area-that-have-created-from-the-equations-above-




Question Number 18681 by Joel577 last updated on 27/Jul/17
y = ∣sin x∣ + 2  y = ∣x∣ + 2 −π  −π ≤ x ≤ π  Find the area that have created  from the equations above
$${y}\:=\:\mid\mathrm{sin}\:{x}\mid\:+\:\mathrm{2} \\ $$$${y}\:=\:\mid{x}\mid\:+\:\mathrm{2}\:−\pi \\ $$$$−\pi\:\leqslant\:{x}\:\leqslant\:\pi \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{that}\:\mathrm{have}\:\mathrm{created} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{above} \\ $$
Answered by ajfour last updated on 27/Jul/17
Commented by ajfour last updated on 27/Jul/17
∫_0 ^(  π) sin xdx=(−cos x)∣_0 ^π =2  Required area= 2+2+(1/2)(2π)(π)                                =π^2 +4 .
$$\int_{\mathrm{0}} ^{\:\:\pi} \mathrm{sin}\:\mathrm{xdx}=\left(−\mathrm{cos}\:\mathrm{x}\right)\mid_{\mathrm{0}} ^{\pi} =\mathrm{2} \\ $$$$\mathrm{Required}\:\mathrm{area}=\:\mathrm{2}+\mathrm{2}+\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2}\pi\right)\left(\pi\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\pi^{\mathrm{2}} +\mathrm{4}\:. \\ $$
Commented by Joel577 last updated on 28/Jul/17
can we solve this without graph?
$$\mathrm{can}\:\mathrm{we}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{without}\:\mathrm{graph}? \\ $$
Commented by ajfour last updated on 28/Jul/17
one way or another, more or less,  the same thing.
$$\mathrm{one}\:\mathrm{way}\:\mathrm{or}\:\mathrm{another},\:\mathrm{more}\:\mathrm{or}\:\mathrm{less}, \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{thing}. \\ $$
Commented by Joel577 last updated on 28/Jul/17
okay, thank you very much
$${okay},\:{thank}\:{you}\:{very}\:{much} \\ $$

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