For example, 1. When studying the displacement problem of an object moving in a straight line at a uniform speed: if the speed of the object changes at any time, how to solve the displacement of the object? At this point, calculus has become our favorable tool. We can infinitely subdivide the motion time of an object. In each case, the change of speed is very small, so we can ignore this small change and think that the object is moving in a straight line at a uniform speed, so we can find the displacement according to the existing knowledge. Then add up all the displacements in time, that is, "infinite summation", and the total displacement can be known. Now we understand that the displacement of an object when it moves in a variable-speed linear motion is equal to the graphic area surrounded by the speed-time image and the time axis; 2. When studying the direction of uniform circle centripetal acceleration; According to Newton's second law, we can know that the acceleration direction of uniform circular motion points to the center of the circle; At the same time, the direction of acceleration can also be determined by using the limit idea. When two points on the circumference are infinitely close, the speed change is infinitesimal, so the base angle of the isosceles triangle enclosed by VAVB△V is close to 90, so the speed change is perpendicular to the speed and the speed is perpendicular to the radius. Therefore, in the uniform circular motion, the direction of acceleration always points to the center of the circle.

3. When studying the problem of variable force doing work, we can directly solve the problem of constant force doing work by using the formula; But for variable force, we can't use the formula; In this case, with the help of calculus, we can subdivide the displacement infinitely. At each small displacement, the force changes very little, which can be regarded as a constant force, and the work done by the output can be calculated according to the formula. Then the work done by each small displacement is infinitely summed, and the total work done by the variable force can be obtained.