When a celestial source of radio waves is scanned with an aerial beam which is much longer than the source in one direction but suitably narrow in the other, the transformation from the true distribution to the measured value is referred to as strip integration. It is here treated as a special case of two-dimensional aerial smoothing in which the aerial beam is allowed to spin about its centre as it moves about the sky. It is shown that the resolution obtainable is set by the cross-sectional profile of the strip beam in the narrow dimension. Thus, when the strip reduces to a line, the resolution is complete and full reconstruction of the true distribution is possible; but scans must be made in all directions. In the general case it is shown that there is a principal solution, and that a finite number of scans suffices to determine it. A method is presented for reconstructing the principal solution from the observed data.