Evaluate the line integral, \int_C z\,dx + x \,dy + y\,dz where C is the curve C: x =...
Question:
Evaluate the line integral, {eq}\int_C z\,dx + x \,dy + y\,dz {/eq} where {eq}C {/eq} is the curve {eq}C: x = t^4, y = t^2, z = t^4, \quad 0 \leq t \leq 1 {/eq}
Line Integral:
The integral, taken along a line, of any function that has a continuously varying value along that line.
Answer and Explanation: 1
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{eq}C: x = t^4, y = t^2, z = t^4, \quad 0 \leq t \leq 1 {/eq}
hence,
{eq}dx=4t^{3}dt, \enspace dy=2t dt, \enspace dz=4t^{3}dt {/eq}
hence...
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