Let C be the curve represented by the equationsx = t, y = 3t2, z = 6t3 (0 t 1)In each

Chapter 15, Problem 12

(choose chapter or problem)

Let \(C\) be the curve represented by the equations

\(x=t, \quad y=3 t^{2}, \quad z=6 t^{3} \quad(0 \leq t \leq 1)\)

In each part, evaluate the line integral along \(C\).

(a)  \(\int_{C} x y z^{2} d s\)

(b)  \(\int_{C} x y z^{2} d x\)

(c)  \(\int_{C} x y z^{2} d y\)

(d)  \(\int_{C} x y z^{2} d x\)

Equation Transcription:

Text Transcription:

C

X = t, y = 3t^2, z = 6t^3,  (0 leq t leq 1)

integral_C xyz^2 ds

integral_C xyz^2 dx

integral_C xyz^2 dy

integral_C xyz^2 dz

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