Let I= _0^ 100 (1- 2 x) d x, then - Vidyadip

MCQ

Let $I=\int_0^{100 \pi} \sqrt{(1-\cos 2 x)} d x$, then

A
$I=0$
✓
$I=200 \sqrt{2}$
C
$I=\pi \sqrt{2}$
D
$I=100$

✓

Answer

Correct option: B.

$I=200 \sqrt{2}$

(B)
$I=\int_0^{100 \pi} \sqrt{(1-\cos 2 x)} d x$
$\begin{array}{l}=\int_0^{100 \pi} \sqrt{2 \sin ^2 x} d x \\ =\sqrt{2} \int_0^{100 \pi} \sin x d x \\ =100 \sqrt{2} \int_0^\pi \sin x d x\end{array}$
$\ldots\left[\because \int_0^{2 a } f (x) d x=2 \int_0^{ a } f (x) d x\right.$, if $\left.f (2 a -x)= f (x)\right]$
$\begin{array}{l}=100 \sqrt{2}[-\cos x]_0^\pi \\ =200 \sqrt{2}\end{array}$

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