   Chapter 10.3, Problem 61E

Chapter
Section
Textbook Problem

# Horizontal and Vertical Tangency In Exercises 29–38, find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. x = 3 t , y = t + 2 0 ≤ t ≤ 4

To determine

To calculate: Area of surface generated by revolving the curve with parametric equations x=3t and y=t+2 on the interval 0t4.

Explanation

Given:

The provided parametric equations are:

x=3t and y=t+2

And the provided interval is:

0t4

Formula used:

If a smooth curve C given by x=f(t) and y=g(t) does not cross itself on an interval atb, then the area S of the surface of revolution about the x-axis is given by:

S=2πabg(t)(dxdt)2+(dydt)2dt

Calculation:

Consider the provided parametric equations:

x=3t and y=t+2

Now, differentiate x with respect to t to get:

dxdt=3 …… (1)

And, differentiate y with respect to t to get:

dydt=1 …… (2)

Now, If a smooth curve C given by x=f(t) and y=g(t) does not cross itself on an interval atb, then the area S of the surface of revolution about the x-axis is given by:

S=2πabg(t)(dxdt)2+(dy<

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