If the area bounded by $ f(x)=\max (\sin x, \cos x) ; 0 \leq x \leq \frac{\pi}{2}, x=\frac{\pi}{2} $ and the coordinates axes is equal to $ k $, then $ [k+3] $ is equal to (where, [.] denotes the greatest integer function

Question

If the area bounded by $ f(x)=\max (\sin x, \cos x) ; 0 \leq x \leq \frac{\pi}{2}, x=\frac{\pi}{2} $ and the coordinates axes is equal to $ k $, then $ [k+3] $ is equal to (where, [.] denotes the greatest integer function, $ 2 $, $ 8 $, $ 4 $, $ 6 $

MARKS App · Accepted Answer

f x = { cos x for 0 ≤ x ≤ π / 4 sin x for π / 4 x ≤ π / 2 ∴ Required Area = 2 ∫ 0 π / 4 cos xdx = 2 sin x 0 π / 4 = 2 sq units ⇒ k = 2 ⇒ k + 3 = 2 + 3 = 4

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