Q10 of 26 Page 1

Evaluate:


Let

Here, f(x) = |x cos πx|




Let





∴ I = I1 + I2 + I3 + I4 …(i)


Firstly, we integrate I1, we get










[∵ sin (-x) = - sin x and cos (-x) = cos x]


[∵ cos π = -1 and sin π = 0]



Now,









[∵ sin (-x) = - sin x and cos (-x) = cos x]


[∵ cos π/2 = 0 ]



Now,

















[∵ cos π = -1 and sin π = 0]




Now, putting the value of I1, I2, I3 and I4 in eq. (i), we get






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