AP EAMCET202420 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
If A x-a + B x+C x^2+b^2 = 1 (x-a) (x^2+b^2 ) then C =
Options
- A-1 a^2+b^2
- B1 a^2+b^2
- C-a a^2+b^2
- Da a^2+b^2
Correct answer
C. -a a^2+b^2
Step-by-step solution
A (x-a) + B x+C x^2+b^2 = 1 (x-a) (x^2+b^2 ) A (x^2+b^2 )+(B x+C)(x-a)=1 (A+B) x^2+(C-a B) x+A b^2-a C=1 On comparing we get, A+B=0 ....(i) C-a B=0 ....(ii) A b^2-a C=1 ....(iii) From (i) and (ii), C+a A=0 A= -C a ; Put A= -C a in equation (iii), -C a b^2-a C=1 -C ( b^2+a^2 a )=1 C= -a a^2+b^2