MHT CET20243 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
2 x^2-1 (x^2+4 ) (x^2-3 ) d x=
Options
- A9 14 ⁻¹ ( x 2 )+ 5 14 3 ( x- 3 x+ 3 )+ c , (where c is constant of integration)
- B9 7 ⁻¹ ( x 2 )+ 5 7 3 ( x- 3 x+ 3 )+ c , (where c is constant of integration)
- C9 7 ⁻¹ ( x 2 )- 5 7 3 ( x- 3 x+ 3 )+ c , (where c is constant of integration)
- D9 14 ⁻¹ ( x 2 )+ 5 7 ( x- 3 x+ 3 )+ c , (where c is constant of integration)
Correct answer
A. 9 14 ⁻¹ ( x 2 )+ 5 14 3 ( x- 3 x+ 3 )+ c , (where c is constant of integration)
Step-by-step solution
aligned & Let I = 2 x^2-1 (x^2+4 ) (x^2-3 ) d x & 2 x^2-1 (x^2+4 ) (x^2-3 ) = A x^2+4 + B x^2-3 & 2 x^2-1= A (x^2-3 )+ B (x^2+4 ) & 2 x^2-1=( A + B ) x^2-(3 ~A -4 ~B ) aligned aligned & A+B=2 and 3 A-4 B=1 & A= 9 7 and B= 5 7 aligned I = 9 7 1 x^2+(2)^2 ~d x+ 5 7 1 x^2-( 3 )^2 ~d x aligned & = 9 7 1 2 ⁻¹ ( x 2 )+ 5 7 1 2 3 ( x- 3 x+ 3 )+ c & = 9 14 ⁻¹ ( x 2 )+ 5 14 3 ( x- 3 x+ 3 )+ c aligned