(6) The integrals represent the volume of a solid. Describe and sketch the solid.(a) √ 2πx³dx2(b) So Tyzdy.1+y²

Given: The volume of solida). b). Aim:To describe and sketch the solidThe formula used:The volume…

Answered: (6) The integrals represent the volume…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Question

(6) The integrals represent the volume of a solid. Describe and sketch the solid.
(a) √ 2πx³dx
2
(b) So Tyzdy.
1+y²

Expert Solution

Step 1: Question

Given:

The volume of solid

a). $integral subscript 0 superscript 1 2 πx to the power of 9 dx$

b). $integral subscript 0 superscript 2 fraction numerator πy over denominator 1 plus y squared end fraction d y$

Aim:

To describe and sketch the solid

The formula used:

The volume $open parentheses V close parentheses$ of a solid generated by revolving the region bounded by $y equals f left parenthesis x right parenthesis$ and the x‐axis on the interval $open square brackets a comma space b close square brackets$ about the x‐axis is

$V equals integral subscript a superscript b straight pi open square brackets straight f left parenthesis straight x right parenthesis close square brackets squared dx$

The volume $open parentheses V close parentheses$ of a solid generated by revolving the region bounded by $x equals f left parenthesis y right parenthesis$ and the y‐axis on the interval $open square brackets a comma space b close square brackets$ about the y‐axis is

$V equals integral subscript a superscript b straight pi open square brackets straight f left parenthesis y right parenthesis close square brackets squared d y$

Power Rule of Integration $integral x to the power of n d x equals fraction numerator x to the power of n plus 1 end exponent over denominator n plus 1 end fraction plus straight c$ , for all real except $negative 1$

$integral fraction numerator f apostrophe open parentheses x close parentheses over denominator f open parentheses x close parentheses end fraction d x equals ln open vertical bar f open parentheses x close parentheses close vertical bar plus c$ , where $c$ is an integration constant.