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AP EAMCET201822 Apr 2018Evening ShiftMathematicsIndefinite IntegrationActual

For x < 1, x-x^2 1-x d x=

Options

  1. A4 3 (1-x)^ 3 / 2 - 2 5 (1-x)^ 5 / 2 -2 1-x +c
  2. B4 3 (1-x)^ 3 / 2 - 2 3 (1-x)^ 5 / 2 -2 1-x +c
  3. C2 3 (1-x)^ 3 / 2 -2 1-x +c
  4. D- 2 15 (1-x)^ 3 / 2 (2+3 x)+c

Correct answer

D. - 2 15 (1-x)^ 3 / 2 (2+3 x)+c

Step-by-step solution

aligned & For x < 1, I= x-x^2 1-x d x= x(1-x) 1-x d x & = x 1-x d x aligned Let 1-x=t^2 array lc & d x=-2 t d t So, & I= (1-t^2 ) t(-2 t) d t=2 (t^4-t^2 ) d t & I=2 [ t^5 5 - t^3 3 ]+c & I= 2 15 t^3 (3 t^2-5 )+c & I= 2 15 (1-x)^ 3 / 2 [3(1-x)-5]+c & I= -2 15 (1-x)^ 3 / 2 (3 x+2)+c . array

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