Definite Integration Question 56
Question 56
- The value of $\int_{1}^{37 \pi} \frac{\pi \sin (\pi \log x)}{x} d x$ is
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Solution:
- Let $I=\int_{1}^{37 \pi} \frac{\pi \sin (\pi \log x)}{x} d x$
Put $\quad \pi \log x=t$
$$ \Rightarrow \frac{\pi}{x} d x=d t $$
$\therefore \quad I=\int_{0}^{37 \pi} \sin (t) d t=-[\cos t]_{0}^{37 \pi}=-[\cos 37 \pi-\cos 0]$
$$ =-[(-1)-1]=2 $$
