AP EAMCET20228 Jul 2022Morning ShiftMathematicsDefinite IntegrationActual
₀^ 2 m x n x d x+ _ - ^ m x n x d x=
Options
- A0 , if m = n and m , n Z
- Bif m=n, m, n Z
- Cif m n, m, n Z
- D2 m, n R
Correct answer
B. if m=n, m, n Z
Step-by-step solution
since f(-x)= m(-x) x(-x) aligned & f(-x)=- x x & =-f(x) aligned f ( x ) is odd function aligned & _ - ^ m x n x d x=0 & I= ₀^ 2 m x n x d x=0 aligned 2 t m = n aligned & = ₀^ 2 ^2 x d x & I=4 ₀^ / 2 ^2 x d x (i) [ ^2 x is over function ] & I=4 ₀^ / 2 ^2 ( 2 -x ) d x aligned I=4 ₀^ / 2 ^2 x d x ...(ii) Adding (i) and (ii) aligned & 2 I=4 ₀^ / 2 1 dx =4 2 =2 & I = aligned