Integral (Trapezoidal rule and mid point rule)

[starstruck_]

Homework Statement

find:

∫13e^(1/x)

upper bound: 2
lower bound: 1

using the trapezoidal rule and midpoint rules
estimate the errors in approximation

Homework Equations

I've done the approximations using the trapezoidal rule and midpoint rule, but I can't figure out how to calculate the error.

this is the formula:
∫f(x)dx = approximation + error


3. The Attempt at a Solution
I need to rearrange the formula to solve for the error so:

error = ∫f(x)dx- approximation the only problem is, i have no idea how to find the integral of ∫13e^(1/x)

this is as far as i can get : 13∫e^(1/x)dx

let u = 1/x
du = -x^-2 dx where x=/= 0

uh not really sure how to work with that once I plug everything in- I don't think I've seen something like this before :/

 

[vela]

You're supposed to estimate the error, not calculate the actual error. Look in your textbook for an expression that gives an upper bound for the error.

 

[Ray Vickson]

Homework Statement

find:

∫13e^(1/x)

upper bound: 2
lower bound: 1

using the trapezoidal rule and midpoint rules
estimate the errors in approximation

Homework Equations

I've done the approximations using the trapezoidal rule and midpoint rule, but I can't figure out how to calculate the error.

this is the formula:
∫f(x)dx = approximation + error 3. The Attempt at a Solution
I need to rearrange the formula to solve for the error so:

error = ∫f(x)dx- approximationthe only problem is, i have no idea how to find the integral of ∫13e^(1/x)

this is as far as i can get : 13∫e^(1/x)dx

let u = 1/x
du = -x^-2 dx where x=/= 0

uh not really sure how to work with that once I plug everything in- I don't think I've seen something like this before :/

Every textbook that covers these topics will also have error bounds that are relatively easy to compute. These will not give the exact values of the error, but will at least give upper bounds; so if the upper bound on the error is smaller than some $\epsilon$ you know that the true (unknown) error is also guaranteed to be less than $\epsilon$. That is always the way these things are done; it would be useless to search for an exact error, since the only way to get it would be to know the exact answer already!