1. Suppose that both the ln and log buttons have fallen off your calculator, but you desperately need to compute a decimal approximation of \(\ln(4)\).
   1. First recall that the \(\ln\) function is defined in terms of an integral. Write down the definite integral that equals \(\ln(4)\).
   2. Use the midpoint rule to estimate the value of \(\ln(4)\) with six equal subintervals. Then use the trapezoid rule to estimate \(\ln(4)\), and then use Simpson’s rule. How much better does each approximation get?
   3. Can you write a computer program to approximate the decimal presentation of \(\ln(4)\)? As a reference, to check your program, past mathematicians have computed \[\ln(4) \approx 1.3862943611198906188344642429163531361510002687\,.\]