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For the following exercises, use a computer algebra system (CAS) to evaluate the line integrals over the indicated path.

$$

[\mathrm{T}] \int_{C}\left(x^{2}+y^{2}+z^{2}\right) d s

$$

$$

C : \mathbf{r}(t)=\sin t \mathbf{i}+\cos t \mathbf{j}+8 t \mathbf{k} \text { when } 0 \leq t \leq \frac{\pi}{2}

$$

$\frac{\sqrt{65}}{6} \pi\left(3+16 \pi^{2}\right)$

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the pyramid is a function is given by or equals to sci fi Cosan, Z and eight. So here's our d s over dt as the model cousin Score plus ones waste one who has a swears 46 64. So we have swirled with Susie five and the integral is given by I'll see we have x square plus voice work Z score D s. Well, then we have zero to have pie one was 64 piece where Times Square with 65 t t in the answer equals two square within 65 over six pi times three plus 16 Paice Warrior

University of Illinois at Urbana-Champaign