Using Trapezoidal or Simpson's to find volume (1 Viewer)

[edmund gosse]

Hello.
I cannot make sense of these two similar questions.

from Cambridge 3 Unit Year 11, p.434, q10.
A cone is generated by rotating the line y=2x about the x-axis between x=0 and x=3. Using the trapezoidal rule with four function values, estimate the volume of the cone.

from Cambridge 3 Unit Year 11, p.437, q10.
The region bounded by the curve y=3^(x-1) and the x-axis between x=1 and x=3 is rotated about the x-axis. Use Simpson's rule with five function values to approximate the volume of the solid that is formed. Give your answer correct to two decimal places.

How do you use the area under a curve to give you the volume of rotation?

Thanks for your time.

 

[khorne]

<s>That's the volume of a region between a curve and x-axis from x= a to x=b around the x-axis...Atleast I think it is (I'm starting out this topic) </s>

ignore me =]

 

[clintmyster]

basically you add the square of all the approximations

 

[kaz1]

Find the appropriate integral and use the approximation on that.

 

[edmund gosse]

basically you add the square of all the approximations

What do you mean, "all the approximations", there's only one, isn't there?

Find the appropriate integral and use the approximation on that.

You mean use trap rule on y=x^2??

 

[kaz1]

You mean use trap rule on y=x^2??

Yes

 

[clintmyster]

What do you mean, "all the approximations", there's only one, isn't there?

basically you find y^2 for each function value and then apply it to the formula

for more info, see the following website:
Math Forum - Ask Dr. Math

 

[edmund gosse]

ok, thanks kaz1 and clintmyster.