JEE Mains · Maths · STD 12 - 7.2 definite integral
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:
- A 10
- B 12
- C 14
- D 16
Answer & Solution
Correct Answer
(B) 12
Step-by-step Solution
Detailed explanation
\(A=\int_0^{\pi / 4} \cos x d x+\int_{\pi / 4}^\pi \sin x d x+\int_\pi^{5 \pi / 4}-\sin x d x+\int_{5 \pi / 4}^{3 \pi / 2}-\cos x d x\) \(A =(\sin x )_0^{\pi / 4}+(\cos x )_\pi^{\pi / 4}+(\cos x )_\pi^{5 \pi / 4}+(\sin x )_{3 \pi / 2}^{5 \pi / 4}\)…
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