Evaluate the line integral, where C is the given curve. \int_C zdx + xdy + ydz \\ C: x = t^3, y...
Question:
Evaluate the line integral, where {eq}\displaystyle C {/eq} is the given curve.
{eq}\displaystyle \int_C zdx + xdy + ydz \\ C: x = t^3, y = t^4, z= t^3, 0 \leq t \leq 1 {/eq}
Integrals:
The Line integral/integral over a specific path is done by rewriting the equation of path in terms of a parameter. The line integral for a given function is depicted as :{eq}\displaystyle \int_C n(x,y)ds {/eq} where C is the trajectory or path of the point describing curve or a line-segment.
Answer and Explanation: 1
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To evaluate the line integral:
{eq}\displaystyle\int_C zdx + xdy + ydz;\\ C: x = t^3, y = t^4, z= t^3, 0 \leq t \leq 1 {/eq}
Now simplifying the...
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Line Integrals: How to Integrate Functions Over Paths
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Chapter 15 / Lesson 2
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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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