AP EAMCET201920 Apr 2019Evening ShiftMathematicsDefinite IntegrationActual
_ e⁻¹ ^ e^2 | x x | d x=
Options
- A2 5
- B2
- C5
- D5 2
Correct answer
D. 5 2
Step-by-step solution
I= _ e⁻¹ ^ e^2 | x x | d x= _ e⁻¹ ^1 (- x x ) d x+ ₁^ e^2 ( x x ) d x On putting x=t d x x =d t aligned & =- _ -1 ^0 t d t+ ₀^2 t d t= [ -t^2 2 ]_ -1 ^0+ [ t^2 2 ]₀^2 & =- 1 2 (0-1)+ 1 2 (4-0)= 1 2 +2= 5 2 aligned Hence, option (d) is correct.