Suppose that the temperature at a point (x, y) in the plane is given by T(x, y) = xye^(−x^2−y^2) .

Explain how the quantity −gradient of T(x, y) is related to the flow of heat in the plane.

Evaluate the integral from 0 to 1 of (gradient of T(x, y)) dot <x, 1> dx and explain what it represents physically.