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Evaluate the line integral $\displaystyle \int_C \textbf{F} \cdot d \textbf{r}$, where $C$ is given by the vector function $\textbf{r} (t)$.$\textbf{F}(x, y, z) = \sin x \textbf{i} + \cos y \textbf{j} + xz \textbf{k}$,$\textbf{r}(t) = t^3 \textbf{i} - t^2 \textbf{j} + t \textbf{k}$, $0 \leqslant t \leqslant 1$

$$\int_{C} \mathbf{F} \cdot d \mathbf{r}=\frac{6}{5}-\cos (1)-\sin (1)$$

Vector Calculus

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Anna Marie V.

Campbell University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

Boston College

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So the value is a line to crow. And, uh, here way, computer. Looking like the previous problem, we come here for far off T That would complete our prime teeth. And we take the we take the dot product integrated and Ortiz a lower point of seo in hwa. So access teach you. So we have thiss Why's that fifty square? Because I see even functions or negativity school cause and in fifties were no cause and he scores the something exorcised force. The road is three t square minus two tea one so integral from zero to one than their products or street he square scientific You minus two t co site is square plus t to the fourth Stickley and then tied the rift. You should be able to see that is straightforward You Some problems take you because you that despises you. So this this should be Detective Cho ce I kill and summer. This should be that if sai t square pastie to the fifth or five. We make sure this derivative to teach those from an active and this one's pretty square. Yeah, So you probably one you get minus co sign one minus sign one plus one over five. You're probably zero you can necked if one my zero plus zero. So this one's reprocess Want aliens or six over five minus coast? I want minus sign one.

Topics

Vector Calculus

Anna Marie V.

Campbell University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

Boston College

Lectures

Join Bootcamp