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Chapter 6: Q. 1 (page 573)

Write down definite integrals to express the given geometric quantities :

The volume of the solid obtained by revolving f(x)on a,b around the x-axis, by the disk method.

Short Answer

Expert verified

Volume of solid with disk cross section along x-axis is =蟺鈭�abfx2dx.

Step by step solution

01

Given Information :

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

02

Definite integral formula by disk method :

The volume of the solid S formed by revolving the region bounded by the curve y=f(x)between x=aand x=babout the x鈭抋xis is given by ,

localid="1654000659093" V=蟺鈭�abf(x)2dx

where, cross section perpendicular to the axis of revolution is in the form of a disk of radius, f(x).

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Most popular questions from this chapter

Sketching disks ,washers and shells : sketch the three disks , washers , shells that result from revolving the rectangles shown in the figure around the given lines

y axis .

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

The centroid of the region between the graph of f(x) = x 2

and the x-axis on [0, 2].

Use antidifferentiation and/or separation of variables to solve each of the differential equations in Exercises 19鈥�28. Your answers will involve unsolved constants.

28.dydx=x2e-y

Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.

dydx=xe鈭�y
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