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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781305266636

Chapter 5, Problem 1P

Textbook Problem

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(a) Find a positive continuous function *f* such that the area under the graph of *f* from 0 to *t* is *A*(*t*) = *t*^{3} for all *t* > 0.

(b) A solid is generated by rotating about the *x*-axis the region under the curve *y* = *f*(*x*), where *f* is a positive function and *x* … 0. The volume generated by the part of the curve from *x* = 0 to *x* = *b* is *b*^{2} for all *b* > 0. Find the function *f*.

(a)

To determine

**To find:** The positive continuous function *f*.

**Given information:**

Area under the graph of *f* from 0 to *t* is

**Calculation:**

Show the Equation of the area under the graph as follows.

Apply the Fundamental Theorem of Calculus, Part 1 as follows.

If *f* is continuous on *g* is defined by

Function *g* is continuous on

(b)

To determine

**To find:** The function *f*.

Single Variable Calculus

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