AP EAMCET20225 Jul 2022Morning ShiftMathematicsDefinite IntegrationActual
[ . ] represents greatest integer function, then _ -1 ^1(x[1+ x]+1) d x=
Options
- A1
- B2
- C5 2
- D3 2
Correct answer
C. 5 2
Step-by-step solution
_ -1 ^1(x[1+ x]+1) d xI= _ -1 ^1(x[1+ x]+1) d x We know that, -1 x 1I= _ -1 ^0(x[1+ x]+1) d x+ ₀^1(x(1+ x)+1) d x aligned & I= _ -1 ^0(x 0+1) d x+ ₀^1(x+1) d x & I=[x]_ -1 ^0+ [ x^2 2 +x ]₀^1 & I=0-(-1)+ [ 1 2 +1 ] & I=2+ 1 2 = 5 2 aligned