Suppose that $f\,\,\left( x \right)\,\,\, \ge \,\,0$ for all $x\,\, \in \,\,\left[ {0,1} \right]$ and $f$ is continuous in $\left[ {{\rm{0,}}\,{\rm{1}}} \right]$ and $\mathop \smallint \nolimits_0^1 \,\,f\left( x \right)\,\,dx = 0$ then $\forall \,\,x\,\, \in \,\,\left[ {0,1} \right],\,\,f$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

Suppose that

f\,\,\left( x \right)\,\,\, \ge \,\,0

for all

x\,\, \in \,\,\left[ {0,1} \right]

and

f

is continuous in

\left[ {\mathrm{0,}\,\mathrm{1}} \right]

and

\int \nolimits_0^1 \,\,f\left( x \right)\,\,dx = 0

then

\forall \,\,x\,\, \in \,\,\left[ {0,1} \right],\,\,f

View answer and explanation

Correct option: C

Constant

Option C (Constant) is correct because if f(x) is non-negative and its integral over [0,1] is 0, then f(x) must be identically zero, hence constant.