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3 ∫ 1 Cos ( Log X ) X D X

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Question

\[\int\limits_1^3 \frac{\cos \left( \log x \right)}{x} dx\]

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Solution

\[Let\ I = \int_1^3 \frac{\cos \left( \log x \right)}{x} d\ x . \]
\[Let\ \log\ x = t . Then, \frac{1}{x} dx = dt\]
\[When\ x = 1, t = 0\ and\ x\ = 3, t = \log 3\]
\[ \therefore I = \int_0^{\ log 3} \cos t d t\]
\[ = \left[ \sin t \right]_0^{\ log 3} \]
\[ = \sin \left( \log 3 \right)\]

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Definite Integrals

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Chapter 19: Definite Integrals - Exercise 20.2 [Page 38]

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

Chapter 19 Definite Integrals
Exercise 20.2 | Q 8 | Page 38

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