# XLPack Solver – Quadrature (semi-infinite interval)

This function computes the numerical integration of the given function over a semi-infinite interval (one of the interval bounds is -∞ or +∞).

Let’s compute the integral of the following example function.

f(x) = 1/(1 + x^2)

The solver program will write the value of x into the variable value cell (B6 in this case). The function value cell (B7 in this case) must contain the formula to compute f(x) from x. To solve this example, the formula is =1/(1+B6^2).

The interval and output range (D7:E12 in this case) is the cell range for one of the bounds a of integration interval [-∞, a] or [a, +∞] (input) and the computed integral (output). Input a in the first column of each row and click “Compute”. Then the value of ∫ f(x) dx [-∞, a] or [a, +∞] will be computed and output to the second column of each line. If the row with a blank cell in the first column is encountered, the computation will be terminated even within the interval and output range.

Qagi or Dehint can be selected as the solver program for semi-infinite integration interval. For special integrand functions, Qawf can be selected.

The standard value of tolerance is 1.0e-8. The tolerance value will be set to EpsAbs and EpsRel of Qagi and Qawf. It will also be set to Eps of Dehint.

For Qawf, further one parameter must be provided.

The cell ranges can be specified as larger than required. In that case, only the necessary range will be used from left upper corner.

Please refer to here for “Save/Restore” button.

When “Help” button is clicked, this page will be displayed if the network connection is available.

The “?” button of right upper corner will not work correctly. Please use “Help” button.