Question

The area under the curve y=|cos x-sin x|, 0≤ x≤ (π)/(2), above the x-axis is

• A. 2√(2)
• B. 2√(2)-2
• C. 2√(2)+2
• D. 0

Hint:

Use symmetry and remove modulus by splitting at sign–change points.

Answer 1

The Correct Option is B

cos x-sin x\ge0 on [0,π/4]. By symmetry, Area=2int₀^π/4(cos x-sin x)dx =2bigl[sin x+cos xbigr]₀^π/4 =2(√(2)-1)=2√(2)-2