(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If [itex]\vec{r}(t) = t^2\vec{i} + t\cos{(\pi t)}\vec{j} + \sin{(\pi t)}\vec{k}[/itex], evaluate [itex]\int_{0}^{1} \vec{r}(t) \text{dt}[/itex].

2. Relevant equations

3. The attempt at a solution

So I tried integrating each individual part, and I got

[itex]\frac{1}{3}t^3\vec{i} + (-\pi t\sin{(\pi t)} - \frac{\sin{(\pi t)}}{\pi})\vec{j} - \frac{\cos{(\pi t)}}{t}\vec{k} |_{0}^{1}[/itex]

(For the coefficient of [itex]\vec{j}[/itex] I used integration by parts, I'm not sure if that's right because it looks weird)

But evaluating at 0 makes the coefficient of [itex]\vec{k}[/itex] undefined! What should I do? Thanks.

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# Homework Help: Find the definite integral of a vector

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