1. ## trapezoidal rule

if the definite integral $\displaystyle \int_1^3 (x^2+1) dx$ is approximated by using the trapezoid rule with n=4, the error is?

2. Originally Posted by yoman360
if the definite integral $\displaystyle \int_1^3 (x^2+1) dx$ is approximated by using the trapezoid rule with n=4, the error is?
Do you know how to use the trapzoid rule?

I would find the trapezoid rule approximation. Then I would evaluate the definite integral. The error would be the difference.

3. Originally Posted by ione
Do you know how to use the trapzoid rule?

I would find the trapezoid rule approximation. Then I would evaluate the definite integral. The error would be the difference.
using trapezoidal rule i got 43/3

using integral i got 32/3

subtract them and o get error=1/12

Correct?

4. Originally Posted by yoman360
using trapezoidal rule i got 43/3

using integral i got 32/3

subtract them and o get error=1/12

Correct?
I got 43/4 using the trapezoidal rule and an error of 1/12

5. Originally Posted by yoman360
if the definite integral $\displaystyle \int_1^3 (x^2+1) dx$ is approximated by using the trapezoid rule with n=4, the error is?
Your textbook or classnotes will have a formula for the size of the maximum error. Please post it and then say what part of it you're having trouble with.

Originally Posted by ione
Do you know how to use the trapzoid rule?

I would find the trapezoid rule approximation. Then I would evaluate the definite integral. The error would be the difference.
The whole point of the trapezoidal rule is to compute definite integrals numerically and to know what the maximum error is in the result for a given value of n.

6. Originally Posted by ione
I got 43/4 using the trapezoidal rule and an error of 1/12
oops i made a typo in my last post. i also got 43/4 using trapezoidal rule