Automated theorem proving in support of computer algebra

Abstract

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Application of Parseval’s Theorem on Evaluating Some Definite Integrals

“…We can obtain the infinite series forms of these definite integrals by using Parseval's theorem; these are the major results of this paper (i.e., Theorems 1 and 2). As for the study of related integral problems can refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. On the other hand, we propose some definite integrals to do calculation practically.…”

Using Area Mean Value Theorem to Solve Some Double Integrals

“…We can obtain the solutions of these double integrals using area mean value theorem; these are the major results of this paper (i.e., Theorems 1-3). Adams et al [1], Nyblom [2], and Oster [3] provided some techniques to solve the integral problems. Yu , Yu and B.…”

Solving Some Definite Integrals by Using Maple

“…We can obtain the closed forms of these two types of definite integrals by using differentiation with respect to a parameter and Leibniz differential rule ; these are the main results of this paper (i.e., Theorems 1, 2). The study of related integral problems can refer to [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Simultaneously, we can compare the method used in this article with that in [27].…”