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Integration can be used to find areas, volumes, central points and many useful things. It is often used to find the area underneath the graph of a function and the x-axis . The first rule to know is that integrals and derivatives are opposites!
Sum Rule \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx Add a constant to the solution \mathrm{If\:}\frac{dF(x)}{dx}=f(x)\mathrm{\:then\:}\int{f(x)}dx=F(x)+C
Integration Rules are the mathematical rules implemented to solve various integral problems. The integration rules are very important to find areas under the curve, volumes, etc., for a large scale.
Integration rules are rules that are used to integrate any type of function. Some of these rules are pretty straightforward and directly follow from differentiation whereas some are difficult and need some integration techniques to get derived.
What Are The Rules of Integration? There are many rules of integration that help us find the integrals. the power rule, the sum and difference rules, the exponential rule, the reciprocal rule, the constant rule, the substitution rule, and the rule of integration by parts are the prominent ones.
In this section, we define integrals over an infinite interval as well as integrals of functions containing a discontinuity on the interval. Integrals of these types are called improper integrals. We examine several techniques for evaluating improper integrals, all of which involve taking limits.
To help us in learning these basic rules, we will recognize an incredible connection between derivatives and integrals. When we differentiate we multiply and decrease the exponent by one but with integration, we will do things in reverse.
In this chapter we will look at several integration techniques including Integration by Parts, Integrals Involving Trig Functions, Trig Substitutions and Partial Fractions. We will also look at Improper Integrals including using the Comparison Test for convergence/divergence of improper integrals.
Integration Rules and Formulas Properties of the Integral: (1) Z b a f(x)dx = Z a b f(x)dx (2) Z a a f(x)dx = 0 (3) Z b a kf(x)dx = k Z b a f(x)dx (4) Z b a [f(x)+g(x)]dx = Z b a f(x)dx+ Z b a g(x)dx (5) Z b a f(x)dx = Z c a f(x)dx+ Z b c f(x)dx (a < c < b) (6) Z b a F0(x)dx = F(b) F(a) (7) d dx Z x a f(t)dt = f(x) (8) d dx Z g(x) a f(t)dt = f ...
Knowing how to use those rules is the key to being good at Integration. So learn the rules and get lots of practice.