Thread: trapezoidal rule

I need to approximate the definite integral using the trapezoidal rule of:
integral(lower bound 1)(upper bound 5) 1/x^2 * dx; n=4

Originally Posted by nystudent2729

I need to approximate the definite integral using the trapezoidal rule of:
integral(lower bound 1)(upper bound 5) 1/x^2 * dx; n=4

$\displaystyle f(x) = \frac{1}{x^2}
$

$\displaystyle \int_1^5 f(x) \, dx \approx \frac{1}{2}\left[f(1) + 2f(2) + 2f(3) + 2f(4) + f(5)\right]
$

I need help finding the trapezoid error estimate of: integral(upper bound 5)(lower bound 1) 1/x^2 *dx; n=4
Thanks.
I know that the formula is M(b-a)^3/12n^2 but I am having trouble understanding how to find M.

Originally Posted by nystudent2729

I need help finding the trapezoid error estimate of: integral(upper bound 5)(lower bound 1) 1/x^2 *dx; n=4
Thanks.
I know that the formula is M(b-a)^3/12n^2 but I am having trouble understanding how to find M.

I assume that this is an upper bound estimate of the error where M is the maximum value of $\displaystyle f''(x)$ over the interval [1, 5] and $\displaystyle f(x) = \frac{1}{x^2}$ ....