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Π / 2 ∫ − π / 2 Sin | X | D X is Equal To(A) 1 (B) 2 (C) − 1 (D) − 2 - Mathematics

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Question

\[\int\limits_{- \pi/2}^{\pi/2} \sin\left| x \right| dx\]  is equal to

Options

  •  1

  • 2

  • − 1

  • − 2

MCQ
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Solution

\[\int_{- \frac{\pi}{2}}^\frac{\pi}{2} \sin\left| x \right| d x\]

\[ = - \int_{- \frac{\pi}{2}}^0 \sin x\ dx + \int_0^\frac{\pi}{2} \sin x\ dx\]

\[ = - \left[ - \cos x \right]_{- \frac{\pi}{2}}^0 + \left[ - \cos x \right]_0^\frac{\pi}{2} \]

\[ = 1 - 0 - 0 + 1\]

\[ = 2\]

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Definite Integrals
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Chapter 20: Definite Integrals - MCQ [Page 118]

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RD Sharma Mathematics [English] Class 12
Chapter 20 Definite Integrals
MCQ | Q 18 | Page 118

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