# calc

posted by .

how big must n be so that the absolute value of the error in using the trapezoid rule is less than .00001?

for the integral (square root of (1+x^4))
where a=0 and b=1

• calc -

Oh dear me, I would have to get my numerical analysis book out of the attic for this error analysis.
I guess I would suggest trying it with a few values of n and seeing how quickly it converges, unless you have a text with the error bound rules handy.

• calc -

OK, I found it online
|E| /= (1/[12 n^2])(b-a)^3 df/dx^3
use the maximum value of the second derivative of the function on the interval a to b, here 0 to 1

• calc -

typo repair
|E| /= (1/[12 n^2])(b-a)^3 d^2f/dx^2

f = (1+x^4)^.5
df/dx = .5 (1+x^4)^-.5 (4 x^3)
= 2 x^3(1+x^4)^-.5
so
d^2/dx^2 = 2 x^3 [ -.5)(4x^3)(1+x^4)^-1.5] + (1+x^4)^-.5 [ 6 x^2]

find the maximum of that between x = 0 and x = 1
n^2 = (1/|12 E|)1^3 times that maximum

## Similar Questions

1. ### Physics/Statistics

We're actually learning propigation of error in my chem class, but it seems to be used equally as much in Physics/Stats. My teacher showed us two methods of doing it: REAL Method (Addition/Subtraction): square root[(error absolute …
2. ### Chemistry

How do you find Absolute error and how do you find relative error?
3. ### Calculus

Find the exact area of the region enclosed by the square root of (x) + the square root of (y) is = 1; x = 0 and y = 0. I moved the first equation around to get: y = [1- the square root of (x) ] ^2 Unfortunately, this gives me bounds …
4. ### calculus

use the power series to estimate the series: from 0 to 4 of ln(1+x)dx with absolute value of the error less than .0001/ Give your estimate of the integral as well as a bound on the error. I found the 'terms' in the series to be: x-(1/2)x^2+(1/3)x^3-(1/4)x^4...... …
5. ### calculus

use the power series to estimate the series: from 0 to 4 of ln(1+x)dx with absolute value of the error less than .0001/ Give your estimate of the integral as well as a bound on the error. I found the 'terms' in the series to be: x-(1/2)x^2+(1/3)x^3-(1/4)x^4...... …
6. ### Calculus - Derivatives

The approximation to a definite integral using n=10 is 2.346; the exact value is 4.0. If the approximation was found using each of the following rules, use the same rule to estimate the integral with n=30. A) Left Rule B) Trapezoid …
7. ### university physics

Derive absolute error in equations: 1)Derive absolute error in (e/m) e/m= 2V/B^2*R^2 2)Derive absolute error in B B=8uN(Inet)/square root 125a