(1) By means of Fourier-cosine transformation and definite integral transformation , the equations governing the boundary problem are converted to a group of singular equations.

(2) A definite integral is an indefinite integral evaluated over an interval.

(3) Fourier cosine, Fourier sine transformation and definite integral transformation simplify the equations of the boundary problem into a group of singular equations.

(4) Therefore, the computation appears very important to the definite integral.

(5) The integral calculus primary coverage includes: Definite integral, indefinite period classification.

(6) The author makes an initial discussion on how to clarify the origin and theoretical basis of infinitesimal method during the teaching of this very method in the application of definite integral.

(7) In this paper, we obtain several theorem of the definite integral of triangle composite function.

(8) The theorem shows how to find the mean value using a definite integral.

(9) The integral calculus basic concept is a circular function indefinite integral and the definite integral.

(10) Given a initial value, a wave packet can be expressed as a definite integral or an improper integral.

(11) This paper shows the important roles of variable upper limit definite integral derivative through several examples.

(12) This article is to make students know and understand the dialectical relation in the calculus by teaching the definition of limit thought, differential coefficient and definite integral.

(13) The improper integral is the limit state of the definite integral.

(14) If the integrand is related to the top integral function in definite integral computation, the definite integral possesses the different expression from.

(15) In this paper, the application of axisymmetric property on the definite integral operation is studied.