21. Holds, then the integrand becomes approximately zero before the interaction-picture density operator changes significantly. 22. Newton Cotes formulae can be useful if the value of the integrand at equally spaced points is given. 23. Integrating it by parts over a spacelike cross section recovers the form of the integrand familiar from canonical quantization. 24. The " n " numbers are the partial information about the true integrand f ( x ). 25. My integrand goes to infinity at the integration boundaries, but the area under the curve is still finite. 26. In such cases, the integrand can be changed to a rational function by using the substitutions of Euler. 27. The momentum wavefunction arises in the integrand since the position and momentum space wavefunctions are Fourier transforms of each other. 28. Numerical integration methods can generally be described as combining evaluations of the integrand to get an approximation to the integral. 29. This is equivalent to locating the peaks of the function from the projections of the integrand onto the coordinate axes. 30. Distributed ray tracing samples the integrand at many randomly chosen points and averages the results to obtain a better approximation.
