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1 ∫ − 1 | 1 − X | D X is Equal to (A) −2 (B) 2 (C) 0 (D) 4 - Mathematics

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Question

\[\int\limits_{- 1}^1 \left| 1 - x \right| dx\]  is equal to

Options

  • −2

  • 2

  • 0

  • 4

MCQ
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Solution

 2

 

\[\int_{- 1}^1 \left| 1 - x \right| d x\]
\[ = \int_{- 1}^0 \left( 1 - x \right) dx + \int_0^1 \left( 1 - x \right) dx\]
\[ = \left[ x - \frac{x^2}{2} \right]_{- 1}^0 + \left[ x - \frac{x^2}{2} \right]_0^1 \]
\[ = 0 + 1 + \frac{1}{2} + 1 - \frac{1}{2} - 0\]
\[ = 2\]

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Definite Integrals
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Chapter 20: Definite Integrals - MCQ [Page 119]

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RD Sharma Mathematics [English] Class 12
Chapter 20 Definite Integrals
MCQ | Q 25 | Page 119

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