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Numerade Educator

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Problem 7 Medium Difficulty

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

$ \displaystyle \int_C (x+ 2y) \, dx + x^2 \, dy $, $ C $ consists of line segments from $ (0, 0) $ to $ (2, 1) $ and from $ (2, 1) $ to $ (3, 0) $

Answer

$$
\frac{5}{2}
$$

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Video Transcript

so line grow. Here we have two parts. First Part's thiss that we call this disco. See what this just called? This seat you and we do both interpreted added together. So that's try to Paramount tries both. Exit was to t y host Titi from there to one see to Mexico's too rusty Wife hosts one minus t. He also goes from zero to one. So that's two C one part first, uh, X plus two wise forty and tease from zero to one, it's prostitute wise forty The axis are to tt ex squares forty square do you wise dt? So we have zero to a one eighty plus forty square. So this was a times one over to because his teeth were over two. And we're pulling what? Plus for Similarly this won t few overthrew, probably while we have one or three. So we got four plus for over three. That's sixteen over three This twelve over three plus for over three in this off another page to do the sea to part of the crew exit host to Krusty. Why horse one minus two So too wise to minus two teams. So you have for my honesty. The Axis ditty X Square is a two plus Otis Corpus forty plus four and the wife is a negative one. TT so just changes toe minus a. Similarly, we, uh, simplify this. Minus t square minus forty, minus two minus five. T minus four class for there's a minus one over three is teachable red three. We probably want minus T score over two point one. The one over two. We got this. So six are two plus fifteen seventeen with a minus sign from So the original integral, original integral fish out. You know, this guy should be the the answer off these Hooper added together. So you're sixteen over three minus seventeen over a six. The first part is thirty two over three star. Sorry to over six social. Fifteen over six. Uh, and then we can divide by syriza five over two