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3 ∫ 1 ∣ ∣ X 2 − 4 ∣ ∣ D X

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Question

\[\int\limits_1^3 \left| x^2 - 4 \right| dx\]

Sum

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Solution

\[\int_1^3 \left| x^2 - 4 \right| d x\]
\[ = \int_1^2 - \left( x^2 - 4 \right) dx + \int_2^3 \left( x^2 - 4 \right) dx\]
\[ = \left[ - \frac{x^3}{3} + 4x \right]_1^2 + \left[ \frac{x^3}{3} - 4x \right]_2^3 \]
\[ = \frac{- 8}{3} + 8 + \frac{1}{3} - 4 + 9 - 12 - \frac{8}{3} + 8\]
\[ = 4\]

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Definite Integrals

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Chapter 19: Definite Integrals - Revision Exercise [Page 122]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12

Chapter 19 Definite Integrals
Revision Exercise | Q 33 | Page 122

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