If we can integrate this new function of u, then the antiderivative of the original function is obtained by replacing u by the equivalent expression in x. Even ...

The important thing to remember is that the integral doesn't change its value if you change the name of the variable throughout.

This reverse process is given the name of integration. In this lesson, we shall study this concept and various methods and techniques of integration. OBJECTIVES.

In every case, the function being integrated is the product of two functions: one is a composite function, and the other is the derivative of the “inner.

Differentiation — as we saw last term, differentiation allows us to compute and study the instantaneous rate of change of quantities.

22 нояб. 2002 г. · Introduction. 5. Chapter 1. Integrals. 6. 1.1. Areas and Distances. The Definite Integral. 6. 1.2. The Evaluation Theorem.

Whereas differentiation determines the slope of a tangent line to a curve, integration determines the area under a curve. 7.1 Antiderivatives. • power rule / xn ...

Let f(x) be a function. Then, the collection of all its primitives is called the indefinite integral of f(x) and is denoted by ∫f(x)dx.

... Notes: The substitution method turns the integral into a simpler integral involving the variable u. The new integral can be evaluated by using either the ...

Integration is the process of finding the area under a graph. An example of an area that integration can be used to calculate is the shaded one shown in the ...