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AP EAMCET202423 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

If [4] x x + [4] x d x= 2 3 [A [4] x^3 +B [4] x^2 +C [4] x +D (1+ [4] x ) ]+K then 2 3 (A+B+C+D)=

Options

  1. A2 3
  2. B- 2 3
  3. C4 3
  4. D- 4 3

Correct answer

B. - 2 3

Step-by-step solution

Let I= [4] x x + [4] x d x Let u= [4] x d u= 1 4 x^ 3 / 4 d x and x =u^2 x=u^4 aligned & I=4 u^3 u+1 d u=4 (u^2-u+1- 1 u+1 ) d u & I= 4 3 u^3- 4 u^2 2 +4 u-4 (u+1)+K & I= 4 3 [4] x^3 -2 [4] x^2 +4 [4] x -4 (1+ [4] x )+K & I= 2 3 [2 [4] x^3 -3 [4] x^2 +6 [4] x -6 (1+ [4] x ) ]+K aligned Comparing with aligned & - [A [4] x^3 +B [4] x^2 +C [4] x +D (1+ [4] x ) ]+K & A=2, B=-3, C=6, D=-6 & 2 3 (A+B+C+D)=- 2 3 aligned

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