The value of the integral ₀^ / 2 ( ¹⁰⁰ x- ¹⁰⁰ x ) d x is

Step-by-step solution

Let I = ₀^ / 2 ( ¹⁰⁰ x- ¹⁰⁰ x ) d x & . I= ₀^ / 2 ¹⁰⁰ ( 2 -x )- ¹⁰⁰ ( 2 -x ) ) d x & [ ₀^ a f(x) d x= ₀^ a f(a-x) d x ] & I= ₀^ / 2 ( 100 x- ¹⁰⁰ x ) d x aligned On adding Egs, (i) and (iii), we get 2 I=0 I=0