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YZ

# 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+x^{3}+5 y^{3}} ; \quad \mathbf{r}(t)=t \mathbf{i}+\frac{1}{3} t^{2} \mathbf{j}+\sqrt{t} \mathbf{k}$$0 \leq t \leq 2$

Integrals

Vectors

Vector Functions

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##### Catherine R.

Missouri State University

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Oregon State University

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University of Michigan - Ann Arbor

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### Video Transcript

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YZ
University of Illinois at Urbana-Champaign

#### Topics

Integrals

Vectors

Vector Functions

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp