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AP EAMCET202421 May 2024Evening ShiftMathematicsDefinite IntegrationActual

₀^1 x (1-x)^ 3 / 4 d x=

Options

  1. A4 5
  2. B8 15
  3. C14 5
  4. D16 5

Correct answer

D. 16 5

Step-by-step solution

aligned & I= ₀^1 x (1-x)^ 3 / 4 d x, x= ^2 d x=2 d & I= ₀^ / 2 ^2 ^ 3 / 2 2 d & =2 ₀^ / 2 (1- ^2 ) d & =t - d =d t aligned I=2 ₁^0 t^2-1 t d t=2 [ 2 5 t^ 5 / 2 -2 5 ]₁^0= 16 5

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