The area enclosed by the curves y = sin x + cos x and y = cos x - sin x over the interval 0 , π 2 is

The area enclosed by the curves y=sinx+cosx and  y = cos x - sin x  over the interval  0 , π 2  is

  1. 4 2 - 1
  2. 2 2 2 - 1
  3. 2 2 + 1
  4. 2 2 2 + 1

Solution

The given curves are y=sinx+cosx & y=cosx-sinx

y 1 = sin x + cos x = 2  sin x + π 4
y 2 = 2 | sin π 4 - x |
So, Required Area=∫0π4sin x+cos x-cos x-sin xdx+∫π4π2sin x+cos x-sin x-cos xdx
2∫0π4sinxdx+2∫π4π2cosxdx
=4-22=222-1.

Asked in: JEE Advanced 2013 (Paper 1)

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