हिंदी

3 ∫ 0 1 X 2 + 9 D X .

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प्रश्न

\[\int\limits_0^3 \frac{1}{x^2 + 9} dx .\]
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उत्तर

\[\int_0^3 \frac{1}{x^2 + 9} d x\]

\[ = \int_0^3 \frac{1}{x^2 + 3^2} d x\]

\[ = \frac{1}{3} \left[ \tan^{- 1} \frac{x}{3} \right]_0^3 \]

\[ = \frac{1}{3}\left( \tan^{- 1} 1 - \tan^{- 1} 0 \right)\]

\[ = \frac{1}{3}\left( \frac{\pi}{4} - 0 \right)\]

\[ = \frac{\pi}{12}\]

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अध्याय 19: Definite Integrals - Very Short Answers [पृष्ठ ११५]

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आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 19 Definite Integrals
Very Short Answers | Q 12 | पृष्ठ ११५

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