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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let the area of the region bounded by the curve
$y = \max{\sin x, \cos x}$, lines $x = 0,; x = \frac{3\pi}{2}$, and the x-axis be $A$. Then $A + A^2$ is equal to ______.
Solution
$A = \int_0^{\pi/4} \cos x,dx + \int_{\pi/4}^{\pi/2} \sin x,dx + \int_{\pi/2}^{5\pi/4} (-\cos x),dx + \int_{5\pi/4}^{3\pi/2} (-\sin x),dx$
$= (\sin x)0^{\pi/4} + (-\cos x){\pi/4}^{\pi/2} + (-\sin x){\pi/2}^{5\pi/4} + (\cos x){5\pi/4}^{3\pi/2}$
$= \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} + 1 + 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = 3$
$\Rightarrow A^2 + A = 9 + 3 = 12$
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