Q115 / 160 · AP EAMCET 2023 (16 May Shift 2) · Mathematics

$\int_0^\pi \frac{\cos x}{\sqrt{1-\sin ^2 x}} d x=$

  • A
    $\pi$
  • B
    $\frac{\pi}{2}$
  • C
    $-\frac{\pi}{2}$
  • Correct answer
    D
    $0$

Solution

Let $I=\int_0^\pi \frac{\cos x}{\sqrt{1-\sin ^2 x}} d x$ $\begin{aligned} & \Rightarrow I=\int_0^\pi \frac{\cos x}{|\cos x|} d x=\int_0^{\pi / 2} \frac{\cos x}{\cos x} d x+\int_{\frac{\pi}{2}}^\pi \frac{\cos x}{-\cos x} d x \\ & =\int_0^{\pi / 2} 1 d x-\int_{\pi / 2}^\pi 1 d x=\frac{\pi}{2}-\frac{\pi}{2}=0\end{aligned}$

Hence, the correct answer is option: 'D'.

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