=∫& lt; 0,π/4 & gt; (cosx-sinx)dx+∫& lt; π/4,π/2 & gt; (sinx - cosx) dx
=[sinx+cosx]& lt; 0,π/4 & gt; +[-cosx-sinx]& lt; π/4,π/2 & gt;
= √2- 1 + √2- 1 = 2(√2- 1)