The area of the region bounded by curves y = sin x , y = cos x and the lines x = 0 , x = 4 π is

Question

The area of the region bounded by curves y = sin x , y = cos x and the lines x = 0 , x = 4 π ​ is

TestHub · Accepted Answer

The required area is given by the integral of the upper curve minus the lower curve between the given limits.

In the interval $x \in [0, \frac{π}{4}]$ , $cos x \geq sin x$ .

Area $= \int_{0}^{π /4} (cos x - sin x) d x$

$= [sin x + cos x]_{0}^{π /4}$

$= (sin \frac{π}{4} + cos \frac{π}{4}) - (sin 0 + cos 0)$

$= (\frac{1}{2} + \frac{1}{2}) - (0 + 1)$

$= 2 - 1$

Answer: $2 - 1$

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