Concept of definite integralDefinition 1. Let be a continuous function defined on divide the interval by the points from to into subintervals. (not necessarily equal width) such that when , the length of each subinterval will tend to zero. In the ith subinterval choose for . If exists and is independent of the particular choice of and , then we have . Remark. For equal width, i.e. divide into equal subintervals of length, i.e. , we have . Choose and or .
|