If F(x, y) = (3xy, 2x^2), evaluate the line integral over C F.dr, where C is the curve shown...
Question:
If {eq}\vec{F}(x, y) = (3xy, \ 2x^2) {/eq}, evaluate {eq}\oint_C \vec{F} \cdot d\vec{r} {/eq}, where C is the curve shown below with positive orientation.
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Positive orientation:
The curve which contains a positive orientation obeys a clockwise or counter clockwise path. The beginning and termination point for the positively oriented curve is alike. The line integral of {eq}F {/eq} on {eq}r\left( t \right) {/eq} is gauged by employing the formula, {eq}\oint\limits_C {\vec F \cdot d\vec r = \int\limits_a^b {\vec F\left( {\vec r\left( t \right)} \right) \cdot \vec r'\left( t \right)dt} } {/eq}.
Answer and Explanation: 1
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- It is given that {eq}\vec F\left\langle {x,y} \right\rangle = \left\langle {3xy,2{x^2}} \right\rangle {/eq} and the curve {eq}C {/eq} is...
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Line Integrals: How to Integrate Functions Over Paths
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Chapter 15 / Lesson 2
293
Line integrals are any integral of a function that can be defined along a given curve in a three-dimensional space. Learn the process of line integration and how they can be used to map paths using parametrizations.
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