3 ∫ 1 Cos ( Log X ) X D X

प्रश्न

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

उत्तर

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

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Definite Integrals

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 8 Q 7 Q 9

अध्याय 19: Definite Integrals - Exercise 20.2 [पृष्ठ ३८]

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

अध्याय 19 Definite Integrals
Exercise 20.2 | Q 8 | पृष्ठ ३८

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