LO 3.4A: Interpret the meaning of a

definite integral within a problem.

According to the fitting formula, the

definite integral was used to obtain the shear energy dissipation of iron tailing powder with different lime doses under different normal stresses, as shown in the following equation:

Different from fractional Lyapunov functional method in [30, 32, 37], an appropriate Lyapunov functional composed of fractional integral and

definite integral terms in the proof of Theorem 11 is presented, and we only need to calculate its first-order derivative to derive stability conditions.

The

definite integral in (20) can be split as follows:

On the other hand, the following program allows students to approximate a

definite integral between two points a and b:

(1)

Definite Integral Calculation for Regular Domain.

the constant of integration vanishes since the integral in G(x) is a

definite integral. On using the relation (2.1), we obtain

Taking their sum and the

definite integral for any closed interval [a,b] yields

The steps of the Chaotic Harmony Search algorithm for calculating numerical value of

definite Integral (CHSINT) are as follows:

It is well-known that for single-fold

definite integral, Gauss quadrature may serve as an accurate numerical approximation in most cases [11].

Nine studies consider representing and defining irrational numbers, student use of Derive software in comprehending and making sense of

definite integral and area concepts, perspectives by mathematicians on teaching and learning proof, case studies from a transition-to-proof course on referential and syntactic approaches to proving, infinite iterative processes and actual infinity, teaching assistants learning how students think, the knowledge base about teaching among teachers of calculus in higher education, modeling students' conceptions, and strategies for controlling the work in mathematics textbooks for introductory calculus.

There are two different ways to write the primitive of a Lagrange 1-form of the form L(t,x(t), [??](t), [??](t))dt: the first one, as a

definite integral,

There are several rules for the approximate evaluation of real

definite integral