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Chapter 6: Q. 6 (page 573)

Write down definite integrals to express the given geometric quantities:

The area of the surface is obtained by revolving fxon a,baround the x-axis.

Short Answer

Expert verified

Surface area offxona,b=2蟺鈭�abfx1+fx2dx

Step by step solution

01

Given Information :

Given that to assume that fxis continuous and differentiable, with a continuous derivative.

02

Definite integral formula for surface area :

The surface area S of the solid of revolution obtained by revolving y=fxaround the x-axis from x=a to x=b is

S=2蟺鈭�abfx1+fx2dx

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Most popular questions from this chapter

Consider the region between f(x)=xand the x-axis on [0,4]. For each line of rotation given in Exercises 27鈥�30, use four disks or washers based on the given rectangles to approximate the volume of the resulting solid.

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29-52.

dydx=xy+x+y+1,y(0)=c

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29鈥�52.

31.dydx=-6x2,y1=3

Solve the initial-value problem

dydx=2y1-5y,y0=1

For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals

蟺鈭�01e2xdxand蟺鈭�01(e2x-1)dx
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