What are Integration Formulas?
The integration formulas have been broadly presented as the following sets of formulas. The formulas include basic integration formulas, integration of trigonometric ratios, inverse trigonometric functions, the product of functions, and some advanced sets of integration formulas. Integration is a way of uniting the parts to find a whole. It is the inverse operation of differentiation. Thus the basic integration formula is
∫ f'(x) dx = f(x) + C
Integration Formulas
Using this, the following integration formulas are derived.
The various integral calculus formulas are
- d/dx {φ(x)} = f(x) <=> ∫f(x) dx = φ(x) + C
- ∫ xn dx = [Tex] \frac{x^{n+1}}{n+1} [/Tex] + C, n ≠ -1
- ∫(1/x) dx = loge|x| + C
- ∫ex dx = ex + C
- ∫ax dx = (ax / logea) + C
More, integral formulas are discussed below in the article,
Note:
- d/dx [∫f(x) dx] = f(x)
- ∫k . f(x) dx = k ∫f(x) dx , where k is constant
- ∫{f(x) ± g(x)} dx = ∫f(x) dx ± ∫g(x) dx
Integration Formulas
Integration Formulas are the basic formulas that are used to solve various integral problems. They are used to find the integration of algebraic expressions, trigonometric ratios, inverse trigonometric functions, and logarithmic and exponential functions. These integration formulas are very useful for finding the integration of various functions.
Integration is the inverse process of differentiation, i.e. if d/dx (y) = z, then ∫zdx = y. Integration of any curve gives the area under the curve. We find the integration by two methods Indefinite Integration and Definite Integration. In indefinite integration, there is no limit to the integration whereas in definite integration there is a limit under which the function is integrated.
Let us learn about these integral formulas, and their classification, in detail in this article.
Table of Content
- Integral Calculus
- What are Integration Formulas?
- Integration Formulas of Trigonometric Functions
- Integration Formulas of Inverse Trigonometric Functions
- Advanced Integration Formulas
- Different Integration Formulas
- Application of Integrals
- Definite Integration Formula
- Indefinite Integration Formula
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