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
$$
\frac{1}{20}
$$
Topics
Vector Calculus
Discussion
Top Calculus 3 Educators
Anna Marie V.
Campbell University
Kayleah T.
Harvey Mudd College
Caleb E.
Baylor University
Kristen K.
University of Michigan - Ann Arbor
Watch More Solved Questions in Chapter 16
Video Transcript
That's computer integral. So half off our tea. It is parking Mexico. Stick you, Andi. Why, It cost his square. So that should keeps you two seven. Why? Who's exit host? A cube. Why host his girls off the second term Should be teaching six on our private T. You just take the repetitive component wise. So? So they're thought for them by the tick goes from zero to one and they're top product. Three Tito Nice. This times this past his time. This which is to Tito. Seven I Yeah. So this one? Yes, we can just three teach ten over ten, so he probably wants to be three over ten. Similarly, this one should be you over hate. And that gives us mission. What should we put it off? Forty Toiled minus ten? No. Yes. So this tour for me, which is won over twenty
Topics
Vector Calculus
Top Calculus 3 Educators
Anna Marie V.
Campbell University
Kayleah T.
Harvey Mudd College
Caleb E.
Baylor University
Kristen K.
University of Michigan - Ann Arbor
