Q. 64.1( 21 Votes )

Evaluate:<i

Answer :

Let

Let f(x) = (1 - x²) sin x cos²x

f(-x) = (1 - (-x)²) sin(-x) cos²(-x)

= -(1 - x²) sin x cos²x

= - f(x)

Hence f(x) is an odd function.

Using if f(x) is an odd function, we get I = 0.

OR

Consider

,

Let

|x|=-x, if x<0

And |x|=x, if x≥0

Hence,

= [-0 - (-1)] + [2 - 0]

= [0 + 1] + [2-0]

= 1 + 2

=3

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