Monte Carlo integration does a better job of estimating the true shadow, as the true shadow is a result of countless "points" of light from the rectangular light source intersecting with our plane/casting a shadow on the floor, not a single point of light. By taking a random point on the light source, we can get an "average" look, with different points on the light source contributing to the shadow. With more samples, presumably the estimation would get closer and closer to the true answer.

Monte Carlo integration does a better job of estimating the true shadow, as the true shadow is a result of countless "points" of light from the rectangular light source intersecting with our plane/casting a shadow on the floor, not a single point of light. By taking a random point on the light source, we can get an "average" look, with different points on the light source contributing to the shadow. With more samples, presumably the estimation would get closer and closer to the true answer.