Posted by **UMich1344** on Monday, September 29, 2008 at 10:05pm.

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 Rule

The section deals with approximation errors of definite integrals.

The error in the first approximation is 1.654. I'm not sure if that is relevant in this problem, but I imagine it would be since that's the topic of the section.

- Calculus - Derivatives -
**Scott**, Monday, February 24, 2014 at 6:15pm
If the original estimate was done by LEFT then the error is inversely proportional to the number of steps and the n = 30 error is (10/30) * -1.654 = -.551, approximately. So the estimate for n = 30 would be -.551 + 4.000 = 3.449

If the original estimate was done by TRAP then the error is inversely proportional to the square of the number of steps and the n = 30 error is (10/30)^2 * -1.654 = -.184, approximately. So the estimate for n = 30 would be -.184 + 4.000 = 3.816

If the original estimate was done by SIMP then the error is inversely proportional to the fourth power of the number of steps and the n = 30 error is (10/30)^4 * -1.654 = -.020, approximately. So the estimate for n = 30 would be -.02 + 4.000 = 3.980

## Answer this Question

## Related Questions

- Calculus - Oil is leaking out of a ruptured tanker at a rate of r = 19e^(2t) ...
- linear approximation - a) Find the linear approximation of the function f(x)=...
- Calculus - Suppose that you can calculate the derivative of a function using the...
- Calculus - Can someone explain to me how to do these? Given the following ...
- Calculus(Urgent help) - f(x)=x^3-3x^2+3x+1 near 2 (at a=2) A. Use Linear ...
- calculus - Estimate 1/(sqrt(82)) using linear approximation and the exact value...
- calculus - use the trapezoidal and simpson's rule to approximate the value of ...
- calculus - use the trapezoidal and simpson's rule to approximate the value of ...
- Calculus - use tangent line approximation (linear approximation) to estimate The...
- calculus - se differential, i.e., linear approximation, to approximate (8.4)^(1/...

More Related Questions