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 A4 is equal to _____

Engineering

Mathematics

Condition for Common Roots

Question

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 A⁴ is equal to ______.

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$A \int_{π / 4}^{5 π / 4} (sinx - cosx) dx$

$= {(- cosx - sinx) |}_{π / 4}^{5 π / 4}$

$= (- (\frac{- 1}{\sqrt{2}}) - (\frac{- 1}{\sqrt{2}})) - (- (\frac{- 1}{\sqrt{2}}) - (\frac{- 1}{\sqrt{2}}))$

$\Rightarrow A = \frac{2}{\sqrt{2}} + \frac{2}{\sqrt{2}} = 2 \sqrt{2}$

$\Rightarrow A^{4} = {(2 \sqrt{2})}^{4} = 16 \times 4 = 64$

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