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Evaluate the line integral, where $C$ is the given curve.

$$\begin{array}{l}{\int_{c} e^{x} d x,} \\ {C \text { is the arc of the curve } x=y^{3} \text { from }(-1,-1) \text { to }(1,1)}\end{array}$$

$\int_{C} e^{x} d x=e-\frac{1}{e}$

Vector Calculus

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Johns Hopkins University

Oregon State University

Harvey Mudd College

University of Nottingham

in this question was asked to determine the light to grow into the X DX on were given the Curve X is equal Toe cube, which birds from negative one negative one. So the first thing we know, the first thing we want to do is we want to write everything in terms of X, since we have a DX. So where do our many points start? Well, they started X equal to negative one, and it goes all the way. The X is equal toe. All right. Now, what's the integral of Weetabix? But I'll eat. The X of the exponential function has this unique property where it's integral under Vivar itself, with the integral of either the X is just even the X with X going from one from negative toe. All right, so we're gonna play in one for one for back. So it's either one minus. Now, get a bargain. Nader. What? Brexit? My speeder. Negative. Now he to the negative one. We could write it as one divided by t. So our final answer ins e minus one