   Chapter 10.3, Problem 65E

Chapter
Section
Textbook Problem

# Surface Area In Exercises 63-68, find the area of the surface generated by revolving the curve about each given axis. x = 2 t , y = 3 t , 0 ≤ t ≤ 3 (a) x-axis(b) y-axis

(a)

To determine

To calculate: The surface area of the curve x=2t,y=3t generated by revolving it about x-axis and within the interval 0t3.

Explanation

Given:

The parametric equations,

x=2ty=3t

And, the interval 0t3.

Formula used:

The surface area of a smooth curve C given by x=f(t) and y=g(t) generated by revolving the curve C about the x-axis within the interval atb is given by formula:

S=2πabg(t)(dxdt)2+(dydt)2dt

Calculation:

Consider the equations,

x=2ty=3t

Differentiate x=2t with respect to ‘t’, to get,

dxdt=2

Differentiate y=3t with respect to ‘t’, to get,

dydt=3

If smooth curve C given by x=f(t)

(b)

To determine

To calculate: The surface area of the curve x=2t,y=3t generated by revolving it about y-axis and within the interval 0t3.

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