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JEE Mains · Maths · STD 12 - 8. Application and integration
The area under the curve \(y = \left| {\cos \,x - \sin \,x} \right|\) , \(0 \leq x \leq\frac{\pi }{2}\), and above \(x-\) axis is
- A \(2\sqrt 2 \)
- B \(2\sqrt 2 - 2\)
- C \(2\sqrt 2 + 2\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(2\sqrt 2 - 2\)
Step-by-step Solution
Detailed explanation
\(y = \left| {\cos x - \sin x} \right|\) Required area \( = 2\int\limits_0^{\pi /4} {(\cos x - \sin x)dx} \) \( = 2\left[ {\sin x + \cos x_0^{\pi /4}} \right]\) \(=2\left[\frac{2}{\sqrt{2}}-1\right]\) \(=(2 \sqrt{2}-2)\) sq. units
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