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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Section
BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Surface Area In Exercises 63-68, find the area of the surface generated by revolving the curve about each given axis.

x = t , y = 4 2 t , 0 t 2

(a) x-axis

(b) y-axis

(a)

To determine

To calculate: The surface area of the curve x=t,y=42t generated by revolving it about x-axis within the interval 0t2.

Explanation

Given:

The parametric equations,

x=ty=42t

And, the interval 0t2.

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=ty=42t

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

dxdt=1

Differentiate y=42t with respect to ‘t’, to get,

dydt=2

If smooth curve C given by x=f(t) and y=g(t) does not cross itself on an interval atb then area S of surface of revolution formed by revolving the curve C about the x

axis is

(b)

To determine

To calculate: The surface area of the curve x=t,y=42t generated by revolving it about y-axis within the interval 0t2.

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