AP EAMCET · Maths · Area Under Curves
The area (in sq. units) of the region bounded by the lines \(x=0, x=\frac{\pi}{2}\) and \(f(x)=\sin x, g(x)=\cos x\) is
- A \(2(\sqrt{2}-1)\)
- B \(2(\sqrt{3}-1)\)
- C \(2(\sqrt{2}+1)\)
- D \(3 \sqrt{2}+1\)
Answer & Solution
Correct Answer
(A) \(2(\sqrt{2}-1)\)
Step-by-step Solution
Detailed explanation
Intersection at \(x=\frac{\pi}{4}\). \(A = \int_{0}^{\frac{\pi}{4}} (\cos x - \sin x) dx + \int_{\frac{\pi}{4}}^{\frac{\pi}{2}} (\sin x - \cos x) dx\) \(A = [\sin x + \cos x]_{0}^{\frac{\pi}{4}} + [-\cos x - \sin x]_{\frac{\pi}{4}}^{\frac{\pi}{2}}\)…
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