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Manipal MET2017MathematicsDefinite Integration

₀^1 x(1-x)¹² d x is equal to

Options

  1. A1 132
  2. B1 156
  3. C1 182
  4. DNone of the above

Correct answer

C. 1 182

Step-by-step solution

aligned & ₀^1 x(1-x)¹² d x = & [ x(1-x)¹³ -13 + ₀^1 (1-x)¹³ 13 d x ]₀^1 = & [ x(1-x)¹³ -13 ]₀^1+ [ (1-x)¹⁴ -14 13 ]₀^1 = & [0-0]+ [0- 1 -14 13 ]= 1 182 aligned

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