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BITSAT 2017
Exam
BITSAT
Year
2017
Subject
Mathematics
Chapter
Area Under Curves

BITSAT 2017 · Mathematics · Area Under Curves

The area under the curve y = | x - x|, 0 ≤ x ≤ (π)/(2) and above X...

The area under the curve y=∣cos⁡x−sin⁡x∣,0≤x≤π2y = \left|\cos x - \sin x\right|, 0 \le x \le \dfrac{\pi}{2} and above XX-axis, is

Options

  1. A222\sqrt{2}
  2. B22−22\sqrt{2} - 2
  3. C22+22\sqrt{2} + 2
  4. D00

Correct answer

B. 22−22\sqrt{2} - 2

Step-by-step solution

Required area =∫0π/2∣cos⁡x−sin⁡x∣dx= {∫}_{0}^{\pi / 2}\left|\cos x - \sin x\right|dx

=∫0π/4(cos⁡x−sin⁡x)dx+∫π/4π/2(sin⁡x−cos⁡x)dx= {∫}_{0}^{\pi / 4}\left(\cos x - \sin x\right)dx + {∫}_{\pi / 4}^{\pi / 2}\left(\sin x - \cos x\right)dx

=sin⁡x+cos⁡x0π/4+−cos⁡x−sin⁡xπ/4π/2= {\sin x + \cos x}_{0}^{\pi / 4} + {- \cos x - \sin x}_{\pi / 4}^{\pi / 2}

=(2−1)−(1−2)=22−2= \left(\sqrt{2} - 1\right) - \left(1 - \sqrt{2}\right) = 2\sqrt{2} - 2

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