   Chapter 10, Problem 55RE

Chapter
Section
Textbook Problem

# Surface Area In Exercises 55 and 56, find the area of the surface generated by revolving the curve about (a) the x-axis and (b) the y-axis. x = 4 t ,       y = 3 t + 1 ,     0 ≤ t ≤ t

(a)

To determine

To calculate: The area of the surface generated by the parametric equation x=t,y=3t for the interval 0t2 when revolved around x-axis.

Explanation

Given:

The parametric equation is x=t,y=3t and the interval 0t2.

Formula used:

The area of the surface generated when the parametric equation x=f(t),y=g(t) when t lies between the interval atb do not cross each other and are revolved around coordinate axes is

When revolved around x-axis:

S=2πabg(t)[f'(t)]2+[g'(t)]2dt when revolved around y-axis:

S=2πabf(t)[f'(t)]2+[g'(t)]2dt

Calculation:

Consider the parametric equation x=t,y=3t and the interval 0t2.

Recall that the area of the surface generated when the parametric equation x=f(t),y=g(t) when t lies between the interval atb do not cross each other and are revolved around coordinate axes is

S=2πabg(t)[f'(t)]2+[g'(t)]2dt

Area o

(b)

To determine

To calculate: The area of the surface generated by the parametric equation x=t,y=3t for the interval 0t2 when revolved around y-axis.

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