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AP EAMCET202316 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

x^2-1 x^3 2 x^4-2 x^2+1 d x=

Options

  1. A1 2 x ^2 2 x ^4+2 x ^2+1 + C
  2. B1 2 x^2 2 x^4-2 x^2+1 +C
  3. C1 2 x ^2 4 x ^4-2 x ^2+1 + C
  4. D1 2 x^2 4 x^4+2 x^2+1 +C

Correct answer

B. 1 2 x^2 2 x^4-2 x^2+1 +C

Step-by-step solution

x^2-1 x^3 2 x^4-2 x^2+1 d x= x^2-1 x^5 x^3 2 x^4-2 x^2+1 x^5 d x= 1 x^3 - 1 x^5 2- 2 x^2 + 1 x^4 d x ...(i) Let 2- 2 x^2 + 1 x^4 =t (0+ 4 x^3 - 4 x^5 ) d x=d t ( 1 x^3 - 1 x^5 ) d x= d t 4 Substituting above values in equation (i), we get x^2-1 x^3 2 x^4-2 x^2+1 d x= d t 4 t = 1 4 t^ 1 / 2 ( 1 2 ) +C= 1 2 (2- 2 x^2 + 1 x^4 )^ 1 / 2 +C= 1 2 x^2 2 x^4-2 x^2+1 +C .

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