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Omni-MATH / Suppose that f is a function on the interval [1,3] such that −1≤f(x)≤1 for all x and ∫₁³f(x) dx=0. How large can ∫₁³(f(x))/(x) dx be?

Problem

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problem

Suppose that ff is a function on the interval [1,3][1,3] such that −1≤f(x)≤1-1 \leq f(x) \leq 1 for all xx and ∫13f(x)dx=0\int_1^3 f(x)\,dx = 0. How large can ∫13f(x)xdx\int_1^3 \frac{f(x)}{x}\,dx be?
Plain-text mathematical notation (without MathML)
Suppose that f is a function on the interval [1,3] such that −1≤f(x)≤1 for all x and ∫₁³f(x) dx=0. How large can ∫₁³(f(x))/(x) dx be?
Original LaTeX notation
Suppose that $f$ is a function on the interval $[1,3]$ such that $-1 \leq f(x) \leq 1$ for all $x$ and $\int_1^3 f(x)\,dx = 0$. How large can $\int_1^3 \frac{f(x)}{x}\,dx$ be?

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Source and history

task_id
f9185788-2687-5285-a4cc-d827eaa9889f
task_key
test--f9185788-2687-5285-a4cc-d827eaa9889f
task_revision_id
1
config / split
/ test

Official source

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