Volume with Simpson's Rule? (1 Viewer)

[Finx]

Just a bit hazy on this one =[

The curve y=2^x is rotated about the x-axis between x = 1 and x = 2. Use Simpson's rule with 3 function values to find an approximation of the volume of the solid formed, correct to 3 significant figures.



Also, if you're bored;

Find: ∫ [(x+2)/√(x+3)]dx

For this one, we were first asked to find the derivative of x√(x+3), which was (3x+6)/(2√(x+3)), but I don't know what to do next =[

Thanks in advance!

 

[Aerath]

Here are my answers. I'm not too sure about the first one though, so please check (if there are answers).

 

[Finx]

Both are right - is the formula for volume just pi*simpson's rule?

I don't quite understand what you did after 'Integrate both sides' ='[

 

[Finx]

Could someone write the formula for finding Volume with Simpson's Rule?

I can see pi*(h/3)[y0^2 +( ______ )+ y2^2]

 

[lolokay]

+4y₁²

same as the normal simpson's rules, but using the areas

 

[Finx]

@Aerath: Thanks so much for writing/scanning/uploading etc, its so helpful to see how things are drawn out and calculated.

@lolokay: Sweet, now I can commit the formula to memory. Also thanks for your help in the other thread ;]

 

[Aerath]

Yeah, sorry for the messy scrawl. That just says 4odd^2, because when you have more than 3 function values, you'll have multiple 'odds' and 'evens'.