AP EAMCET202124 Aug 2021Evening ShiftMathematicsIndefinite IntegrationActual
If 3 x-2 x 4 x+5 x d x=A |5 x+4 x|+B x+c , then A and B are
Options
- AA= 22 41 and B= -7 41
- BA= -22 41 and B= 7 41
- CA= -22 41 and B= -7 41
- DA= 22 41 and B= 7 41
Correct answer
D. A= 22 41 and B= 7 41
Step-by-step solution
We have, 3 x-2 x 4 x+5 x d x=A (5 x+4 x)+B x+c On differentiating both sides, we get 3 x-2 x 4 x+5 x = A(-5 x+4 x) 4 x+5 x +B 3 x-2 x 4 x+5 x = -5 A x+4 A x+4 B x+5 B x 4 x+5 x 3 x-2 x=(4 B-5 A) x+(5 B+4 A) x Equating the coefficient of x and x , we get 5 B+4 A=3 and 5 A-4 B=2 Solving, we get A= 22 41 and B= 7 41