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Evaluate the line integral, where $C$ is the given curve.$\displaystyle \int_C e^x \, dx$, $C$ is the arc of the curve $x = y^3$ from $(-1, -1)$ to $(1, 1)$

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

Vector Calculus

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Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Kristen K.

University of Michigan - Ann Arbor

Boston College

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Video Transcript

So if value it is hit the girl actually host y Q So men go xy horse Why? And he goes from negative What to what Then we pocketing this integral We'LL be t from the fifth one toe one It was accessed ese the ex this three squares So we already well this come from here So this is also the sem ist minus one to what I ask because is independent Souto Kwong Co u substitution But I'm going to use X here but it was a Cubist original X and X goes from one to one and this is nothing but the ex So they did this middle step Step me Maybe unnecessary But anyway just to make it clear about the standard procedure this will be He's with X t X and we know how to do this. We should have Onda had the rover TV is still eat with Axl. We have eaten what? Minus each with a negative one And that should be the problem. The answer of the problem

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Topics

Vector Calculus

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Kristen K.

University of Michigan - Ann Arbor

Boston College

Lectures

Join Bootcamp