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# Evaluate the line integral, where $C$ is the given curve.$\displaystyle \int_C (x/y) \, ds$, $C: x = t^3$, $y = t^4$, $1 \leqslant t \leqslant 2$

## $\frac{1}{48}\left(73^{3 / 2}-25^{3 / 2}\right)$

Vector Calculus

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##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

light to grow. So every place wait goes from T from twenty two x over wise one over this computer. Yes, Horse square. Root off the ex titties are three three square square plus the white It is forty cube square Wei have thiss street square square forty two square Let's try to simplify this. We pour tea to the force I excited Square us so often squirrel becomes T square on this will be team we have nine Plus this's our sixteen Peter six. We'LL report it to the fourth So sixteen square TT and can we use a u substitution and you won't are thirty two. So this will be you goes from when Thi's one is twenty five. But his two this is off sixty four plus nine. So seventy three and, uh, he hated his one over search you do you And this is this's you to the one over two. So we have you two is three over two times to over three, so should be won over forty eight here. So this will be one over forty eight seventy three to three over to minus twenty five to three over too

#### Topics

Vector Calculus

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp