2 ∫ 1 Log X D X

प्रश्न

\[\int\limits_1^2 \log\ x\ dx\]

उत्तर

\[Let\ I = \int_1^2 \log\ x\ d\ x\ . Then, \]
\[I = \int_1^2 1 \log x\ d\ x\]
\[\text{Integrating by parts}\]
\[ \Rightarrow I = \left[ x \log x \right]_1^2 - \int_1^2 \frac{1}{x} x\ d\ x\]
\[ \Rightarrow I = \left[ x \log x \right]_1^2 - \int_1^2 d x\]
\[ \Rightarrow I = \left[ x \log x \right]_1^2 - \left[ x \right]_1^2 \]
\[ \Rightarrow I = 2 \log 2 - 2 + 1\]
\[ \Rightarrow I = 2 \log 2 - 1\]

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Definite Integrals

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 32 Q 31 Q 33

पाठ 19: Definite Integrals - Exercise 20.1 [पृष्ठ १७]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12

पाठ 19 Definite Integrals
Exercise 20.1 | Q 32 | पृष्ठ १७

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