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KCET2012MathematicsDefinite Integration

_ / 6 ^ / 3 ³ x ³ x+ ³ x d x is equal to

Options

  1. A2
  2. B3
  3. C12
  4. D6

Correct answer

D. 6

Step-by-step solution

Let I= _ / 6 ^ / 3 ³ x ³ x+ ³ x d x aligned &= _ / 6 ^ / 3 ³ ( 3 + 6 -x ) ³ ( 3 + 6 -x )+ ³ ( 3 + 6 -x ) d x &= _ / 6 ^ / 3 ³ ( 2 -x ) ³ ( 2 -x )+ ³ ( 2 -x ) d x &I= _ / 6 ^ / 3 ³ x ³ x+ ³ x d x aligned On adding Eqs. (i) and (ii), we get aligned 2 I &= _ / 6 ^ / 3 ³ x+ ³ x ³ x+ ³ x d x &=[x]_ / 6 ^ / 3 &= 3 - 6 = 2 - 6 = 6 aligned

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