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Evaluate : 3 ∫ 2 3 X D X . - Mathematics

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प्रश्न

Evaluate : 

\[\int\limits_2^3 3^x dx .\]
योग
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उत्तर

\[I = \int_2^3 3^x \]
\[ = \left.\frac{3^x}{\log3}\right|_2^3 + C .............\left(Use: \int a^x = \frac{a^x}{\log a} + C\right)\]
\[ = \frac{3^3}{\log3} - \frac{3^2}{\log3} + C\]

\[= \frac{1}{\log3}( 3^3 - 3^2 ) + C\]
\[ = \frac{1}{\log3}(27 - 9) + C\]
\[ = \frac{1}{\log3}(18) + C\]

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Definite Integrals
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अध्याय 20: Definite Integrals - Very Short Answers [पृष्ठ ११६]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 20 Definite Integrals
Very Short Answers | Q 36 | पृष्ठ ११६

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