Question

Me again. My answers to subsequent questions involving simpson's rule keep coming out just slightly smaller than the answers in the book. What is happening?

Answer 1

do ahead and post your work; otherwise we have no idea what could be going awry

Answer 2

So, question: Use Simpson's rule with a. 5 ordinates b. 10 ordinates to find approximations for \[\int\limits_{2}^{0} \frac{ 1 }{ 1 + x ^{2} } dx\].

Answer 3

So my workings for a:

Answer 4

just curious, are your limits upside down on that integral?

Answer 5

= 1/2(0.4)(1 + 2(values of y added together, with the exception of the first and last) + 0.2)
=0.2(1.2 + 2(2.16257))
=0.2(1.2 + 4.32514)
=0.2(5.52514)
=1.105028
(Sorry yes, my limits are upside down)

Answer 6

\[\int\limits_{0}^{2}\frac{ 1 }{ 1 + x ^{2} }\]

Answer 7

your values seem to be fine, rounding introduces errors tho; but it your book says round ..

Answer 8

The book says the answer is 1.1051 rounded to four decimal places. I have tried the question with 10 decimals, but it doesn't seem to change my answer.

Answer 9

\[-cos(n\pi)/2+1/2 = \{0,1,0,1,0,1,0,1,...\}\]
\[-cos(n\pi)/2+1/2+1 = \{1,2,1,2,1,2,1,2,...\}\]
\[2^{-cos(n\pi)/2+3/2} = \{2,4,2,4,2,4,2,4,...\}\]

Answer 10

if we let n start at 1 we get the 4,2,4,2,4,2,4 ... coeffs to work up a formula to dbl chk some work

Answer 11

Ok, then: (1/3)(0.4)(1 + 4(0.86207) + 2(0.60976) + 4(0.40984) + 2(0.28090) + 0.2)
= 0.4/3(1.2 + 6.86896)
= 0.4/3(8.06896)
= 1.07586133

Answer 12

Let me just do that again...

Answer 13

No I still get = 1.07586133. Am I doing it right?

Answer 14

i dont think your table has enough reference points