🤔 Find out what you don't know with free Quizzes 🤔Start Quiz Now! # Integrate $f(x, y, z)=x+\sqrt{y}-z^{2}$ over the path $C_{1}$ followed by $C_{2}$ from (0,0,0) to (1,1,1) (see accompanying figure) given by$$\begin{array}{ll}C_{1}: & \mathbf{r}(t)=t \mathbf{i}+t^{2} \mathbf{j}, \quad 0 \leq t \leq 1 \\C_{2}: & \mathbf{r}(t)=\mathbf{i}+\mathbf{j}+t \mathbf{k}, \quad 0 \leq t \leq 1\end{array}$$(GRAPH CANT COPY)The paths of integration for Exercises 15 and 16

## $\frac{1}{6}(5 \sqrt{5}+9)$

Integrals

Vectors

Vector Functions

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#### Topics

Integrals

Vectors

Vector Functions

##### Top Calculus 3 Educators ##### Lily A.

Johns Hopkins University ##### Heather Z.

Oregon State University  ##### Samuel H.

University of Nottingham

Lectures

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