is the direction at the point in which the temperature is decreasing the most rapidly.
And a line integral in a gradient vector field is independent of the path taken. All that matters is the starting point and ending point.
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.
is the direction at the point in which the temperature is decreasing the most rapidly.
And a line integral in a gradient vector field is independent of the path taken. All that matters is the starting point and ending point.