Area between the curves $y=\sin x$ and $y=\lfloor \sin x \rfloor$ from $x=0$ to $x=2\pi$ is...
- $\pi$
- $>3$
- $4$
- $\sin^{-1} a + \cos^{-1} a + \tan^{-1} b + \cot^{-1} b$ for $a\in[-1,1], b\in \mathbb R$
Area between the curves
-2
$\begingroup$
calculus
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2What do you mean by $[\sin x] $?? – 2017-01-07
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0Integral part of sin x – 2017-01-07
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0$\lfloor \sin x \rfloor $ is discontinuous at $x=\pi/2, \pi, 3\pi/2$. – 2017-01-07
1 Answers
1
Hint: Since $\lfloor\sin x\rfloor$ is either $0$ or $-1$ except at discrete points, this is just $$\int_0^{\pi}\sin x\; dx + \int_{\pi}^{2\pi}(1+\sin x)\;dx $$ Can you compute that?