If `| int_(a)^(b) f(x)dx|= int_(a)^(b)|f(x)|dx,a ltb,"then " f(x)=0` has

Options

A. exactly one root in (a,b)
B. at least one root in (a,b)
C. no root in (a,b)
D. none of these

Answer

C

Explanation

We have,
`|underset(a)overset(b) intf(x)dx|leunderset(a)overset(b) int|f(x)|dx` and the equality occurs only if the graph of `y=f(x)` les entirely above or eblow the x-axis for all `x in (a,b)`
Thus, `f(x)=0` has no real root in (a,b)