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AP EAMCET202421 May 2024Evening ShiftMathematicsDefinite IntegrationActual

₀^ / 4 x^2 (x x+ x)^2 d x=

Options

  1. A2- 2+
  2. B4- 4+
  3. C6- 6+
  4. D8- 8+

Correct answer

B. 4- 4+

Step-by-step solution

aligned & I= x^2 (x x+ x)^2 d x & = (x x) ( x x (x x+ x)^2 ) d x & =x x (-1) (x x+ x) & - ( x+x x x) -1 (x x+ x) d x aligned aligned & = -x x (x x+ x) + ^2 x d x & = -x x x x+ x + x= -x+ ^2 x(x x+ x) x(x x+ x) & = -x ^2 x+ x x x(x x+ x) = x-x x x x+ x & ₀^ / 4 x^2 (x x+ x)^2 d x= [ x-x x x x+ x ]₀^ / 4 = 4- 4+ . aligned

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