Question

Can someone show me how to use Simpson's Rule in integral (1/(x+1)^2)dx from 1 to 3?

Answer 1

\[\int\limits_{1}^{3} \frac{ x }{(x+1)^2 }dx\]

Answer 2

Never heard of it before.

Answer 3

Ok, here's Simpson's Rule:

\[\int\limits_a^b f(x) dx \approx \frac{b-a}{6}(f(a)+4f(\frac{a+b}{2})+f(b))\]

So in your case:

\[\int\limits_1^3\frac{x}{(x+1)^2} dx \approx \frac{1}{3}(0.25+\frac{8}{9}+\frac{3}{16} )\]

Plug and chug.

Answer 4

My teacher never taught Simpson's rule, so I looked at my textbook and I found the formula but since the formula is

Answer 5

Oh, that's the composite Simpson's Rule. It goes 2, 4, 2, 4, etc.

Answer 6

it's n = 4

Answer 7

so it just repeats 2,4,2,4,2,4....until x(n) term right?

Answer 8

Right, so for n = 4, it would be 1, 2, 4, 1

Answer 9

ok thanks. that's all i needed. :)

Answer 10

Great, have fun integrating :P

Answer 11

haha thanks :D