Q. 10

Evaluate:</

Answer :

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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