Tài liệu tham khảo các dạng bài tập liên quan đến các vấn đề trong tích phân. Đây là các dạng bài tập tích phân được trình bày theo hình thức tiếng Anh. | Chapter 5e Integral of Irrational Function 8/ 5 7 * 9 9 12 14 15 * 16 * 17 * 18 20 * 21 * 22 23 25 25 26 28 30 31 32 34 35 36 39 40 40 41 41 42 42 42 43 44 45 45 46 47 * 47 48 49 50 50 51 52 53 54 55 55 58 59 61 61 62 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: So choosing u and v such that is wrong. *
