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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 $\textbf{r} (t)$.$\textbf{F}(x, y, z) = (x + y^2) \textbf{i} + xz \textbf{j} + (y + z) \textbf{k}$,$\textbf{r}(t) = t^2 \textbf{i} + t^3 \textbf{j} - 2t \textbf{k}$, $0 \leqslant t \leqslant 2$

## 8

Vector Calculus

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compute this line to grow. So this is the same. Is it great? From the to F off our off t got our private TT So we just have to compute these to quality. So what this f off our off t we replace expert he square wife. I take you up, see by negative duty. So access T square. Why is thi cube so bisque? Worse? Tito six hex is, um negative two cubes. Why process t Q minus Tootie and our private T We just computed component wise So two t hi plus three t squared J minus two k is Yeah then you quickly children, is everything is correct now And that should be the case. So this so integral should be taking the dark brother. So we just do it component wise we are to Teke you plussed fut seven These two term minus six It was the fifth Onda less minus tooty too. You are forty so this can sew something here. No teachers Eight over four minus Teo Teo six plus Hey square from zero to two. We just have the problem. Tubules problem zero Everything is zero two to the eight over two squirrels to the six, which should be sixty four minus sixty for class off time superstate, which give us eight, Elsa answer.

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Vector Calculus

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