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is the statement true/false.

Let $f$ be a continuous integrable function of $\mathbb{R}$ such that either $f(x) > 0$ or $f(x) + f(x + 1) > 0$ for all x$ \in \mathbb{R}$. Then $\int_{-\infty}^{\infty} f(x)dx>0$

is the above statement is true please help someone.

i am sorry that i could not wright it properly.the ingration will be from -infinity to infinity.thanks for help.

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    Consider integrating in both sides of $f(x)>0$ and $f(x)+f(x+1)>0$.2012-09-25

3 Answers 3