trapezoidal rule

**nystudent2729** · Dec 18th 2008, 01:35 PM

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

**skeeter** · Dec 18th 2008, 02:14 PM

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

$f(x) = \frac{1}{x^2}<br />$

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

**nystudent2729** · Dec 18th 2008, 06:38 PM

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.

**mr fantastic** · Dec 18th 2008, 11:08 PM

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 $f''(x)$ over the interval [1, 5] and $f(x) = \frac{1}{x^2}$ ....

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