MHT CET202120 Sep 2021Evening ShiftMathematicsIndefinite IntegrationActual
2 x^2-1 x^4-x^2-20 d x=
Options
- A1 5 | x + 5 x - 5 |+ ⁻¹ ( x 2 )+ c
- B1 2 5 | x + 5 x - 5 |+ ⁻¹ ( x 2 )+ c
- C1 2 5 | x - 5 x + 5 |+ 1 2 ⁻¹ ( x 2 )+ c
- D1 2 | x - 5 x + 5 |+ 1 2 ⁻¹ ( x 2 )+ c
Correct answer
C. 1 2 5 | x - 5 x + 5 |+ 1 2 ⁻¹ ( x 2 )+ c
Step-by-step solution
Let I= 2 x^2-1 x^4-x^2-20 d x If x^2=t , then 2 x^2-1 x^4-x^2-20 = 2 t-1 t^2-t-20 Let 2 t-1 (t-5)(t+4) = A (t-5) + B (t+4) aligned & 2 t -1=( t +4) a +( t -5) B & 2= A + B and -1=4 ~A -5 ~B aligned Solving, we get B =1, ~A =1 I= [ 1 x^2-5 + 1 x^2+4 ] d x= 1 2 5 | x- 5 x+ 5 |+ 1 2 ⁻¹ ( x 2 )+c