Intergration Qs and Simpson's Rule Help Please

[nonsenseTM]

INTEGRATION QUESTIONS
First of all, could any one of give me a thorough explaination of all the versions of Simpson's Rule?

and the answers to these which I need to check
1 Calculate the area enclosed by the curve y=3x-x^2 and the x axis

2 The arc of the curve y=2x^2 -1 between where x=1 and x=3 is rotated about the y axis. Find the volume of the solid formed

 

[boxhunter91]

people have different ways of performing simpsons rule My method is:
h/3(1st + Last +4(odds) + 2(evens)
In a table of values to know which goes where under each box i would do
1,4,2,4,2,4,2,1 So the first and last are one and the number next is 4 then 2-->1

Q1. You dont need simpsons for this.
First find point of intersection with x axis which (0,0) and (3,0)
Then integrate from 3-1(3x-x^2) dx

Q2.It is rotated around the Y axis so you need (x^2)
.: y+1=2x^2
.:x^2=(Y+1)/2
You will need to find the values of Y at x =1 and x=3 which y=1 and y=17
.: Integrate from 17-1((y+1)/2) dy.

 

[nonsenseTM]

could you write down the exact answer for both of them ? coz I got a different answer the one in the book

I might not be very clear about my questions, I know what the formula is but I need the explainations/proof and Q1 and Q2 are just random integration questions

 

[nonsenseTM]

buMP

 

[boxhunter91]

woops made a mistake in number one its from 3-0.
The answer is
4.5 for first.
80 for second.

 

[shady145]

Could somebody please check if this is right...Thanks!

Intergrate: e^2x = .5ln(e^2x+4) + C
________
e^2x+4

what is that for?
integration of e^2x however is (e^2x)/2 +c

 

[nonsenseTM]

woops made a mistake in number one its from 3-0.
The answer is
4.5 for first.
80 for second.

the answer at the back IS wrong
I think forgot the piE

 

[boxhunter91]

Sorry bout that lol.
Yeh 80pi