AP EAMCET202317 May 2023Evening ShiftMathematicsDefinite IntegrationActual
If x^3 1+x^2 d x=A (1+x^2 )^ 3 2 +B (1+x^2 )^ 1 2 +C , then A + B =
Options
- A2 3
- B- 2 3
- C1 3
- D- 1 3
Correct answer
B. - 2 3
Step-by-step solution
x^3 1+x^2 d x= A (1+x^2 )^ 3 / 2 + B (1+x^2 )^ 1 / 2 +c ...(i) x^3 1+x^2 d x= x^2 x 1+x^2 d x Let 1+x^2=t^2 x d x=t d t x^3 1+x^2 d x= (t^2-1 ) t t d t= (t^2-1 ) d t= t^3 3 -t+c x^3 1+x^2 d x= 1 3 (1+x^2 )^ 3 / 2 - (1+x^2 )^ 1 / 2 + c ...(ii) From eq ^ n (i) & (ii), we get aligned & A= 1 3 , B=-1 & A+B= 1 3 -1=- 2 3 aligned