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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

The area bounded by the curve y = | ^ - 1 (sin x)| + |(π)/(2) -...

The area bounded by the curve y=y =\left|\cos^{- 1}\left(sin x\right)\right| + \left|\dfrac{\pi}{2} - cos^{- 1}\left(cos x\right)\right| and the& xx -axis, where π2≤x≤π\dfrac{\pi}{2} \le x \le \pi, is equal toThe area bounded by the curve y = | ^ - 1 (sin x)| + |(π)/(2) - cos^ - 1 (cos x)| and the& x -axis, where (π)/(2) ≤ x ≤

Options

  1. Aπ2{\pi}^{2}
  2. Bπ22\dfrac{{\pi}^{2}}{2}
  3. Cπ28\dfrac{{\pi}^{2}}{8}
  4. Dπ24\dfrac{{\pi}^{2}}{4}

Correct answer

D. π24\dfrac{{\pi}^{2}}{4}

Step-by-step solution

y = \left|\dfrac{\pi}{2} - sin^{- 1}sin x\right| + \left|\dfrac{\pi}{2} - cos^{- 1}cos x\right|<br/>For<br/>Forx \in \left[\dfrac{\pi}{2}, \pi\right]
y = \left|\dfrac{\pi}{2} - \left(\pi - x\right)\right| + \left|\dfrac{\pi}{2} -x\right|
y = \left| x - \dfrac{\pi}{2}\right| + \left|\dfrac{\pi}{2} - x\right|<br/><br/>y = x - π2+\dfrac{\pi}{2} + x - π2=2x−π<br/><imgsrc="/api/proxy−image?url=https\dfrac{\pi}{2} =2x - \pi <br/><img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fnta_abhyas%252Fjee_main%252Fimages%252F85eb0766-7cfe-4eac-b777-3b47f41b005a.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fnta_abhyas%2Fjee_main%2Fimages%2F85eb0766-7cfe-4eac-b777-3b47f41b005a.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fnta_abhyas%2Fjee_main%2Fimages%2F85eb0766-7cfe-4eac-b777-3b47f41b005a.png?alt=media" style="width:1.92708in;height:1.06042in"> <br/>Area =\dfrac{1}{2} \times \dfrac{\pi}{2} \times \pi <br/>=\dfrac{{\pi}^{2}}{4}
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