Since the si is up for months during the summer at the north pole, why is is the equator actually gets the most solar radiation over the cource of a year?

The north pole receives daylight for about 6 months. But there occur the differences in the absorption of incoming solar radiation between the places near the equator and the places near the poles.

At the equator, the sunlight is directly incident on the earth's surface, as a result of which the solar energy had to travel a shorter distance to reach the earth's surface. So the equatorial region receives the highest amount of solar radiation throughout the year.

On the other hand, the places away from the equator receive comparatively lesser amount of radiation and is minimum at the poles. It is because the sun rays are not directly incident on these regions and they had to travel a longer distance to reach the surface.