WEBVTT
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okay. What we want to dio is we want
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to evaluate, um, over the curve on the
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line integral of X y plus, why play Z
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d s? Um, along the curve R t
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is equal to to t i plus t j plus
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to minus two tea. Okay. And t t
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goes from 0 to 1 inclusive. Okay, so
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the first thing we need to do is we know
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that d s is equal to the magnitude of e
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of T. Um d t. And so first
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thing we need to do is we know that the
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of t is equal to the derivative, um,
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of that curve r t. So this is gonna
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be equal to two i plus J minus two K
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. And so, um, the magnitude of e
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of t is equal to the square root of t
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squared plus one squared plus a native to squared.
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And so this is gonna give me, um three
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. Um, and so Gs is equal to three
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d t. Okay, so this is gonna be
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the integral from 0 to 1. Um, X
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is to t. Why is t and Z is
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T minus two t and three D t so that
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seeing a girl we want to do, um,
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so this is gonna be equal to, um,
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three times, integral from 0 to 1. Ah
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, to t squared minus t plus two tt.
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So this is gonna be three times 2/3 t cute
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, minus 1/2 t squared, plus to t evaluated
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, um, 0 to 1. And so when
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we do that, um, we should get 13
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house.