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# Evaluate the line integral, where $C$ is the given curve.$\displaystyle \int_C xy^4 \, ds$, $C$ is the right half of the circle $x^2 + y^2 = 16$

## $$\int_{C} x y^{4} d s=\frac{8192}{5} \approx 1638.4$$

Vector Calculus

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##### Lily A.

Johns Hopkins University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

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### Video Transcript

so yeah, we paramour tries the circle first, use our standard form. Now we wanted right health of this circle. So the ankle goes from active pilot for three to pie over too. It's the easiest way to terrible choices by the standard para militarization of the circle at the right health. So t goes from that pie over too. Hi! Over too. So let's do this. And that may be easier to compute P s first. The exit is negative for coast that square sixteen cose I scurti And the idea is for Kasai. Sorry, The first time should be sixteen Science Corti seven term is the review is for homicide here and scores for sixteen cause I security So insides just inside a square root is just sixteen. So scare of sixes for soldiers got forty. So yeah, if or into grow for Maya's pie over to pie over too. X is for co side white with the force is is fourth with the force scientist and the S is for four years forty that poor old unnecessary stuff or to the six it's our heroes have force Power Coast sai forthe Tea co sign And this is also use our problem. We just let you go society them cause I I'll beat you so if you assign me than negative twenty goes from their pirate Hutu power to it goes from you goes from that one to one. Now we have you to the force. Oh, just sign for them And this do you? So in the fourth with six times, use the fifth over five miles. What to what? And you probably want your wonder whatever. Five plus one over five. The children are fine. So two times four through six over five and you can simplify it. No, I guess I could do that. Two to the thirteen to the ten is a dollar twenty four to the thirty ve I remember. Cora, please. They want night too. Over five. Okay, anyway, is just a simplification part and the key part of the properties in the set up

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#### Topics

Vector Calculus

##### Lily A.

Johns Hopkins University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp