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## Homework Statement

Use the composite trapezoidal sum rule to evaluate

I = integral from 0 to 1 of: (exp(x)-1)/x

At x = 0 the integrand evaluates to 1.

Select the step size h in order to guarantee an approximation error less than

10e-5.

Carry out your calculation with at least 10 decimal significant figures.

Note: the exact answer rounds to

1:31790215145440389486:

## Homework Equations

I know that i need to find the max of f''(x), but it goes to infinity as x goes to zero. How do i find this max value?

## The Attempt at a Solution

Using the Trapezoidal Sum rule with n=1, the error using the Newton Cotes Method is: (10e-5)=(1/12)*f''(x)*h^2

So h = sqrt((12*10e-5)/f''(x))

f''(x) = ((x^2 -2x+2)*exp(x)-1)/(x^3)

I tried L'Hopitals rule, but that gave me 1/3 as x goes to zero, which is incorrect.