For the definite integral problem, the basic solution is to find the original function according to the topic, then bring it into the upper and lower limits of the integral, and finally subtract it to get the answer. For example, to find the definite integral of y=2x from 0 to 1, first find out that its original function is y=x? +c(c is a constant), in order to solve it conveniently, we usually take c=0, and then bring it into the upper and lower limits of the integral, that is, y( 1)-y(0)= 1. For the definite integral problem of the function with difficult derivation, we can consider using the geometric meaning of the function to calculate it, such as finding y=√a? -x？ In the definite integral on (m, n), the integrand is deformed first, x? +y？ =a？ It can be seen that it is a circle, so the problem of finding the definite integral of this function is transformed into the problem of finding the area of the closed figure surrounded by the circle and y=m, y=n and X axis. In addition, it should be noted that the area above the X-axis is positive, and the area below the X-axis is negative, which can be directly added or subtracted in calculation. For this problem, it is difficult to deduce, and geometric meaning can be considered to solve it. The integrand function is a circle with the center at the origin and the radius of 1. Its definite integral on (0,-1) is the area of a closed graph surrounded by a circle and Y = 0, and Y =- 1 is the area of 1/4 circle. Note that this area is above the x-axis.