The area, enclosed by the curves $y = \sin x + \cos x{\rm{ }}\,\,{\rm{and}}\,\,{\rm{ }}y = |\cos x - \sin x|$ and the lines $x = 0,\,\,x = \frac{\pi }{2},$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The area, enclosed by the curves

y = \sin x + \cos x\mathrm{ }\,\,\mathrm{and}\,\,\mathrm{ }y = |\cos x - \sin x|

and the lines

x = 0,\,\,x = \frac{\pi }{2},

View answer and explanation

Correct option: A

2\sqrt 2 (\sqrt 2 - 1)

Option A (

2\sqrt 2 (\sqrt 2 - 1)

) is correct because it represents the area between the curves, calculated by integrating the difference of the functions over the given interval.

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