💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here! # Evaluate the line integral, where $C$ is the given curve.$\displaystyle \int_C x^2y \, ds$, $C: x = \cos t$, $y = \sin t$, $z = t$, $0 \leqslant t \leqslant \pi/2$

## $$\frac{\sqrt{2}}{3}$$

Vector Calculus

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##### Top Calculus 3 Educators ##### Lily A.

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Idaho State University

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### Video Transcript

we're through this light the crow. So first way Haven't the DSR first funeral for this? Yes. So d x d t is negative side he Teo wide Tichy is co sign T please is one so yes should be squared off Science qwerty plus coz I scurti plus y squared tichy on the square root off to TT So we just do the integral he from zero to pie over too X square is coz I scurti side yes square root of to dt or use a U substitution. So cause I tease we said you host co society So this one No bu square and science the negative sign titties to you We have minor square root of to you squared you when she goes from zero to pie over too co signed he goes from from one to zero So it's a semi zero to one square root of to you squared you I got you cube over three employing one So you just got square root of two times one over Siri #### Topics

Vector Calculus

##### Top Calculus 3 Educators ##### Lily A.

Johns Hopkins University ##### Heather Z.

Oregon State University  ##### Michael J.

Idaho State University

Lectures

Join Bootcamp