CUET · MATHS · PYQ PAPER 2023
The area bounded by the curve \(y =\sin x\) between \(x =0\) and \(x =2 \pi\) is
- A 4 sq.units
- B \(4 \pi\) sq.units
- C \(0\)
- D 2 sq.units
Answer & Solution
Correct Answer
(A) 4 sq.units
Step-by-step Solution
Detailed explanation
Area = \(\int_{0}^{2\pi} |\sin x| dx\) Area = \(\int_{0}^{\pi} \sin x dx + \int_{\pi}^{2\pi} (-\sin x) dx\) Area = \([-\cos x]_{0}^{\pi} + [\cos x]_{\pi}^{2\pi}\) Area = \((-\cos \pi - (-\cos 0)) + (\cos 2\pi - \cos \pi)\) Area = \((1+1) + (1-(-1))\) Area = \(2 + 2 = 4\)
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