anonymous
  • anonymous
Integration
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Find the volume generated when each shaded region is rotated through 360 degree about the x-axis.
anonymous
  • anonymous
1 Attachment
Zale101
  • Zale101
What method will you be using? Shell or disk?

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anonymous
  • anonymous
what is shell and what is disk?
Zale101
  • Zale101
|dw:1447574737054:dw|
Zale101
  • Zale101
|dw:1447574798239:dw|
anonymous
  • anonymous
i use this formula \[\int\limits_{b}^{a}\Pi~x^2dx\]
Zale101
  • Zale101
|dw:1447574851080:dw|
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
This is my working but i'm not sure whether my answer is correct.
Zale101
  • Zale101
Disk Method formula \[v=\int\limits_{a}^{b} \pi [f(x)]^2 dx\] Is that what you did?
anonymous
  • anonymous
yes
Zale101
  • Zale101
|dw:1447575366916:dw|
Zale101
  • Zale101
Okay. The way you set up your integral is incorrect.
Zale101
  • Zale101
f(x) is not x \(f(x)=(x-1)^2\)
Zale101
  • Zale101
@MARC_ you there?
anonymous
  • anonymous
yes
Zale101
  • Zale101
the disc formula for solving the volume is by \(V=\int\limits_{a}^{b} \pi [f(x)]^2 dx\) You had \(\int\limits_{b}^{a}\Pi~x^2dx\)
Zale101
  • Zale101
Your f(x)=(x-1)^2. Correct?
anonymous
  • anonymous
yes
Zale101
  • Zale101
How did get x^2 when your function is (x-1)^2?
anonymous
  • anonymous
so it is x^2-2x+1
Zale101
  • Zale101
\(v=\int\limits_{a}^{b} \pi [f(x)]^2 dx\) \(v=\int\limits_{a}^{b} \pi [(x-1)^2]^2 dx\)
Zale101
  • Zale101
\(v=\int\limits_{a}^{b} \pi (x-1)^4 dx\)
Zale101
  • Zale101
Makes sense?
anonymous
  • anonymous
yes
Zale101
  • Zale101
Next is getting your limit intervals. Do you remember on how to do that?|dw:1447576102356:dw|
Zale101
  • Zale101
|dw:1447576194714:dw| Look at where the intervals from the x-axis that makes a bounded spot.
Zale101
  • Zale101
|dw:1447576253295:dw| The outline i drew is your closed interval
Zale101
  • Zale101
|dw:1447576355974:dw| a and b are your limit intervals.
anonymous
  • anonymous
a=0,b=1
anonymous
  • anonymous
is it correct?
Zale101
  • Zale101
Yes
Zale101
  • Zale101
Your integral is all set now :)
anonymous
  • anonymous
\[\int\limits_{0}^{1}\Pi(x-1)^4dx\]
Zale101
  • Zale101
Yes
anonymous
  • anonymous
okay
Zale101
  • Zale101
You're going to learn about the washers method. It's similar but with a slight changes due to the shape. |dw:1447576837801:dw||dw:1447576842933:dw|
Zale101
  • Zale101
|dw:1447576847684:dw|