4. Consider the functions f(x) = ax and g(x)%3 ax, where a>0 is a real number; let R be the regionin the first quadrant that is enclosed by these two functions. When R is rotated about the x-axis, the167Find the average value of the function g(x) = ax over the21volume of the solid formed isinterval fromx=0 to x=5.

Name: 4. Consider the functions f(x) = ax and g(x)%3 ax, where a>0 is a rea
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Description: 4. Consider the functions f(x) = ax and g(x)%3 ax, where a>0 is a real number; let R be the regionin the first quadrant that is enclosed by these two functions. When R is rotated about the x-axis, the167Find the average value of the function g(x) =

Answered: Consider the functions f(x) = ax and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Consider the functions f(x) = ax and g(x)%3 ax, where a>0 is a real number; let R be the region
in the first quadrant that is enclosed by these two functions. When R is rotated about the x-axis, the
167
Find the average value of the function g(x) = ax over the
21
volume of the solid formed is
interval fromx=0 to x=5.

Expert Solution

Step 1

given functions are

$f (x) = a x^{3}, g (x) = a x, a > 0$

only in first quadrant, $x \geq 0, y \geq 0$ , Rotated about x-axis and volume is $\frac{16 π}{21}$ .

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