?(a) Sketch the curve C with parametric equationsx = cos t y = sin t z = sin t 0 ? t ?

Chapter 16, Problem 24

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QUESTION:

(a) Sketch the curve C with parametric equations

x = cos t        y = sin t        z = sin t        0 ⩽ t ⩽ 2𝜋

(b) Find ∫C 2xe2y dx + (2x2e2y + 2y cot z)dy − y2csc2z dz.

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QUESTION:

(a) Sketch the curve C with parametric equations

x = cos t        y = sin t        z = sin t        0 ⩽ t ⩽ 2𝜋

(b) Find ∫C 2xe2y dx + (2x2e2y + 2y cot z)dy − y2csc2z dz.

ANSWER:

Step 1 of 3

The parametric equation of the given curve is

We know that

It follows

Again, we have

Therefore, the given curve lies between the intersection of the circle  with radius 1 unit centered at origin and the plane .

The graph is shown below.

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