Suppose that $f(x) \geq 0$ for all $x \in \lbrack 0,1\rbrack$ and $f$ is continuous in [0,1] and $\int_{0}^{1}{f(x)dx = 0,}$ then $\forall\ x \in \lbrack 0,\ 1\rbrack,\ f$ is

Question

Dr. Abubacker · Accepted Answer

(c)
Let $I = \int_{0}^{1}{f(x)dx = 0}$ and $f(x) \geq 0 \Rightarrow f(x) = 0$

Q. Suppose that $f(x) \geq 0$ for all $x \in \lbrack 0,1\rbrack$ and $f$ is continuous in [0,1] and $\int_{0}^{1}{f(x)dx = 0,}$ then $\forall\ x \in \lbrack 0,\ 1\rbrack,\ f$ is

Explanation

Reviewed by Dr. Abubacker

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