Tích phân 5

Tài liệu Tích phân 5: Chapter 5e Integral of Irrational Function 8/ For evaluating integral we can make a trigonometric change of variables: * with m, n, p is rational number. The Russian mathematicant Trebushep prove that the upper integral only can be expressed in elementary function in 3 follow cases: 1/ p is an interger, when that, put with s is the least common multiple of m, n. 2/ is an interger, put with s is the denominator of p. 3/ is an interger, put with s is the denominator of p. We have the formula: is a n degree polynomial, is a n – 1 degree polynomial with indefinite coefficients To determine p and coefficients of , we take derivative (1) and equate coefficients of two sides to obtain system of equations. (How to prove this formula?) * * * * We have: I = The area of plane figure bounded by the graph and Ox. And is a half circle with radius R = 1. We have the follow figure: I = area of yellow part = area of sector AOB + area of triangle BOC * The second method: S...