Dhaka-2 Higher Secondary 2013 / 10
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Find the area of the region of all points satisfying the inequalities \(x^2 + y^2 \leq 16\) and \(sin (x+y) \leq 0\).
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Re: Dhaka-2 Higher Secondary 2013 / 10
For every pair of $(x,y)$ which satisfies $\sin (x+y) \leq 0$ there is exactly one that satisfies $\sin (x+y) \geq 0$, so the area is half of that of the circle $x^2+y^2 = 16$, or $8 \pi$.
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