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KCET2024MathematicsDefinite Integration

_ - ^ (1-x^2 ) x ^2 x d x is

Options

  1. A- ^2 3
  2. B2 - ^3
  3. C- ^3 2
  4. D0

Correct answer

D. 0

Step-by-step solution

Let f(x)= (1-x^2 ) x ^2 xf(-x)= (1-(-x)^2 ) (-x) ^2(-x)= (1-x^2 )(- x) ( ^2 x )=- (1-x^2 )( x) ( ^2 x ) So, f(x)=-f(-x) So, f(x) is an odd function. Hence, _ - ^ (1-x^2 ) x ^2 x d x=0

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