- #1

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**Problem:**

Let ##\vec{F}## be a vector function defined on a curve C. Let ##|\vec{F}|## be bounded, say, ##|\vec{F}| ≤ M## on C, where ##M## is some positive number. Show that ##|\int\limits_C\ \vec{F} \cdot d\vec{r}| ≤ ML ## (L=Length of C).

**Attempt at a Solution:**

I honestly have no idea where to start with this one. It's not really clear to me exactly what the question is asking me to show.

I understand we have this vector function ##\vec{F}=F_1 \hat{i} + F_2 \hat{j} + F_3 \hat{k} ##, and that's about it... What does it mean to say that the magnitude ##|\vec{F}| ## is "bounded" in such a way that ##|\vec{F}| ≤ M##? Are we imposing a restriction here?

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