SATHEE: Indefinite Integration 1 Question 56

Indefinite Integration 1 Question 56

57. The value of $\int_{1}^{37 π} \frac{π \sin (π \log x)}{x} d x$ is

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Solution:

Let $I = \int_{1}^{37 π} \frac{π \sin (π \log x)}{x} d x$

Put $π \log x = t$

$\Rightarrow \frac{π}{x} d x = d t$

$∴ I = \int_{0}^{37 π} \sin (t) d t = - [\cos t]_{0}^{37 π} = - [\cos 37 π - \cos 0]$

$= - [(- 1) - 1] = 2$

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Indefinite Integration 1 Question 56

57. The value of ∫137ππsin⁡(πlog⁡x)xdx is

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57. The value of $\int_{1}^{37 π} \frac{π \sin (π \log x)}{x} d x$ is