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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Area Under Curves

NDA 2022 · Mathematics · Area Under Curves

What is the area of the region enclosed in the first quadrant by...

What is the area of the region enclosed in the first quadrant by x2+y2=π2,y=sin⁡xx^2+y^2=\pi^2, y=\sin x and x=0x=0 ?

Options

  1. Aπ34−1\frac{\pi^3}{4}-1
  2. Bπ34−2\frac{\pi^3}{4}-2
  3. Cπ32−1\frac{\pi^3}{2}-1
  4. Dπ24−2\frac{\pi^2}{4}-2

Correct answer

B. π34−2\frac{\pi^3}{4}-2

Step-by-step solution


Required area =14π(π)2−∫0πsin⁡xdx=π34−[−cos⁡x]0π=π34−2=\frac{1}{4} \pi(\pi)^2-\int_0^\pi \sin x d x=\frac{\pi^3}{4}-[-\cos x]_0^\pi=\frac{\pi^3}{4}-2
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