AP EAMCET202315 May 2023Evening ShiftMathematicsIndefinite IntegrationActual
₀^ 4 ^2 x ^2 x+4 ^2 x d x=
Options
- A4 + 2 3 ⁻¹ 2
- B- 3 - 2 3 ⁻¹ 3
- C- 12 + 2 3 ⁻¹ 2
- D6 - 2 3 ⁻¹ 4
Correct answer
C. - 12 + 2 3 ⁻¹ 2
Step-by-step solution
aligned & Let I= ^2 x ^2 x+4 ^2 x d x & = ^2 x 3 ^2 x+1 d x= ^2 x ( ^2 x+1 ) (4 ^2 x+1 ) d x aligned Let u= x d u= ^2 x d x aligned & I= d u (u^2+1 ) (4 u^2+1 ) = ( 4 / 3 4 u^2+1 - 1 / 3 u^2+1 ) d u & 2 3 ⁻¹(2 u)- 1 3 ⁻¹(u)+c aligned Now ₀^ / 4 ^2 x ^2 x+4 ^2 x d x= 2 3 ⁻¹(2)- 12