AP EAMCET20228 Jul 2022Evening ShiftMathematicsDefinite IntegrationActual
_ - / 2 ^ 2 ⁻¹( x) d x=
Options
- A15 ^2 / 8
- B- ^2 / 8
- C-7 ^2 / 8
- D7 ^2 / 8
Correct answer
B. - ^2 / 8
Step-by-step solution
I= _ - / 2 ^ 2 ⁻¹( x) d x= _ - / 2 ^ / 2 ⁻¹( x) d x+ _ / 2 ^ 3 / 2 ⁻¹( x) d x+ _ 3 / 2 ^ 2 ⁻¹( x) d x aligned & = _ - / 2 ^ / 2 x d x+ _ / 2 ^ 3 / 2 ( -x) d x+ _ 3 / 2 ^ 2 (-2 +x) d x & = [ x^2 2 ]_ - / 2 ^ / 2 + [ x- x^2 2 ]_ / 2 ^ 3 / 2 + [-2 x+ x^2 2 ]_ 3 / 2 ^ 2 & =0+ 3 ^2 2 - 9 ^2 8 - ^2 2 + ^2 8 -4 ^2+2 ^2 aligned +3 ^2- 9 ^2 8 = ^2+ ^2- 17 ^2 8 =2 ^2- 17 ^2 8 =- ^2 8