Wolfram Research, Inc.

Problem 2

What is the value of to 7 significant digits?

Result

Method 1: Use a built-in function.

The most natural approach gives the correct result but with a warning message.

To guarantee the required digits and to avoid the message, we use arbitrary-precision arithmetic, allow more recursive subdivisions at the right endpoint, and use a more appropriate integration method.

Method 2: Substitute to get a nicer integrand.

We make the substitution . Using , this is equivalent to . This makes the integrand much better behaved, getting rid of any subdivision problems.