JEE Mains · Maths · STD 12 - 8. Application and integration
The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area \(A\). Then \(A ^{4}\) is equal to ............
- A \(64\)
- B \(72\)
- C \(49\)
- D \(81\)
Answer & Solution
Correct Answer
(A) \(64\)
Step-by-step Solution
Detailed explanation
\(A=\int_{\pi / 4}^{5 \pi / 4}(\sin x-\cos x) d x\) \(=\left.(-\cos x-\sin x)\right|_{\pi / 4} ^{5 \pi / 4}\) \(=\left(-\left(\frac{-1}{\sqrt{2}}\right)-\left(\frac{-1}{\sqrt{2}}\right)\right)-\left(-\left(\frac{1}{\sqrt{2}}\right)-\left(\frac{1}{\sqrt{2}}\right)\right)\)…
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