AP EAMCET202022 Sep 2020Evening ShiftMathematicsDefinite IntegrationActual
_ / 6 ^ / 3 1 1+ x d x=
Options
- A12
- B6
- C4
- D13
Correct answer
A. 12
Step-by-step solution
_ / 6 ^ / 3 1 1+ x d x=I I= _ / 6 ^ / 3 x x + x d x We have, _a^b f(x) d x= _a^b f(a+b-x) d x gathered a+b-x= 2 -x I= _ / 6 ^ / 3 ( 2 -x ) ( 2 -x ) + ( 2 -x ) d x I= _ / 6 ^ / 3 x x + x d x gathered Eqs. (i) + (ii) 2 I aligned & = _ / 6 ^ / 3 ( x x + x + x x + x ) d x & = _ / 6 ^ / 3 ( x + x x + x ) d x & = _ / 6 ^ / 3 1 d x=(x)_ / 6 ^ / 3 = ( 3 - 6 ) 2 I & = 6 I= 12 aligned Hence, option (1) is correct.