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NDA2018MathematicsDefinite IntegrationActual

What is ₀^1 x(1-x)^9 d x equal to?

Options

  1. A1 110
  2. B1 132
  3. C1 148
  4. D1 240

Correct answer

A. 1 110

Step-by-step solution

aligned & ₀^1 x(1-x)^9 d x & = ₀^1(1-x)(1-(1-x))^9 d x ( ₀^a f(x) d x= ₀^a f(a-x) d x ) & = ₀^1(1-x) x^9 d x= ₀^1 (x^9-x¹⁰ ) d x & = ( x¹⁰ 10 - x¹¹ 11 )₀^1= 1 10 - 1 11 = 11-10 110 = 1 110 aligned

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