Indefinite Integration 1 Question 56
57. The value of $\int _1^{37 \pi} \frac{\pi \sin (\pi \log x)}{x} d x$ is
Show Answer
Solution:
- Let $I=\int _1^{37 \pi} \frac{\pi \sin (\pi \log x)}{x} d x$
Put $\quad \pi \log x=t$
$$ \Rightarrow \frac{\pi}{x} d x=d t $$
$\therefore \quad I=\int _0^{37 \pi} \sin (t) d t=-[\cos t] _0^{37 \pi}=-[\cos 37 \pi-\cos 0]$
$$ =-[(-1)-1]=2 $$
