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### In Exercises $43-46,$ use a CAS to perform the fo…

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YZ
University of Illinois at Urbana-Champaign
Problem 43

# In Exercises $43-46,$ use a CAS to perform the following steps to evaluate the line integrals.a. Find $d s=|\mathbf{v}(t)| d t$ for the path $\mathbf{r}(t)=g(t) \mathbf{i}+h(t) \mathbf{j}+$ $k(t) \mathbf{k} .$b. Express the integrand $f(g(t), h(t), k(t))|\mathbf{v}(t)|$ as a function of the parameter $t .$c. Evaluate $\int_{C} f d s$ using Equation $(2)$ in the text.$$f(x, y, z)=\sqrt{1+30 x^{2}+10 y} ; \quad \mathbf{r}(t)=t \mathbf{i}+t^{2} \mathbf{j}+3 t^{2} \mathbf{k} 0 \leq t \leq 2$$

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