_0^ 100 | x| d x= ________. - Vidyadip

MCQ

$\int_0^{100 \pi}|\cos x| d x=$ ________.

✓
200
B
100
C
50
D
$0$

✓

Answer

Correct option: A.

200

(A)
Let $I =\int_0^{100 \pi}|\cos x| d x$
$=200 \int_0^{\frac{\pi}{2}}|\cos x| d x$
$\ldots\left[\because \int_0^{2 a } f (x) d x=2 \int_0^{ a } f (x) d x\right.$, if $\left.f (2 a -x)= f (x)\right]$
Since $\cos x$ is positive in the interval $\left(0, \frac{\pi}{2}\right)$
$\therefore I =200 \int_0^{\frac{\pi}{2}} \cos x d x$
$\begin{array}{l}=200[\sin x]_0^{\frac{\pi}{2}} \\ =200\end{array}$

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