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BITSAT2012MathematicsIndefinite IntegrationActual

Evaluate: x 4- x ³ dx

Options

  1. A2 3 ⁻¹ ( x^ 3 / 2 2 )+c
  2. B2 3 ⁻¹ (x^ 3 / 2 )+c
  3. C2 ⁻¹ ( x^ 3 / 2 2 )+c
  4. D1 3 ⁻¹ ( x ^ 3 / 2 2 )+ c

Correct answer

A. 2 3 ⁻¹ ( x^ 3 / 2 2 )+c

Step-by-step solution

I= x 4-x³ d x= x d x 4-x³ Here integral of x = 2 3 x^ 3 / 2 and 4-x³=4- (x^ 3 / 2 )² Put x^ 3 / 2 =t x d x= 2 3 d t So I= 2 3 d t 4-t² = 2 3 ⁻¹ ( x^ 3 / 2 2 )+c

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