   Chapter 16, Problem 24RE

Chapter
Section
Textbook Problem

(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.

(a)

To determine

To Sketch: The curve C with parametric equations x=cost , y=sint , z=sint .

Explanation

Given data:

x=cost , y=sint , z=sint , 0t2π .

Formula used:

Write the expression for circle.

x2+y2=r2 (1)

Here,

r is the radius.

Write the expression for trigonometric function.

sin2x+cos2x=1

Find the value of r using equation (1).

Substitute cost for x and sint for y in equation (1),

cos2t+sin2t=r2

Substitute 1 for cos2t+<

(b)

To determine

To find: The value of C2xe2ydx+(2x2e2y+2ycotz)dyy2csc2zdz

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