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Numerade Educator

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Problem 19 Medium Difficulty

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) = xy^2 \textbf{i} - x^2 \textbf{j} $,
$ \textbf{r}(t) = t^3 \textbf{i} + t^2 \textbf{j} $, $ 0 \leqslant t \leqslant 1 $

Answer

$$
\frac{1}{20}
$$

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