Area and Volume of Generated Solids

[DiscordUser]

 

[Deleted member 4993]

View attachment 27345

I would first calculate the points of intersections of the curves with the line x = π/2 and x-axis. This will provide the limits of integration.

Then I would use disk method - the disks (elemental volume) being parallel to the x-axis.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[nasi112]

(a)
area [MATH]= \int_a^b (A - B)\ dx[/MATH]
What are [MATH]a[/MATH] and [MATH]b[/MATH]?
What are [MATH]A[/MATH] and [MATH]B[/MATH]?

(b)
volume [MATH]= \pi\int_a^b (A - B)^2 \ dx[/MATH]
What are [MATH]a[/MATH] and [MATH]b[/MATH]?
What are [MATH]A[/MATH] and [MATH]B[/MATH]?

(c)

volume [MATH]= \frac{\pi}{2}\int_a^b \left(\frac{A - B}{2}\right)^2 \ dx[/MATH]
What are [MATH]a[/MATH] and [MATH]b[/MATH]?
What are [MATH]A[/MATH] and [MATH]B[/MATH]?

 

[lex]

(b)
volume [MATH]= \pi\int_a^b (A - B)^2 \ dx[/MATH]

?

 

[nasi112]

?

Oh thanks for noticing my mistake

it should be

volume = [MATH]\pi \int_a^b A^2 - B^2 \ dx[/MATH]