Did you know that you can find the value of integral functions with the help of a particular stream of mathematics which is known as Calculus? This is an advanced form of operation that requires a thorough knowledge of properties of numbers. There are mainly two processes that are used by the method of calculus to derive the properties of integrals and derivatives and these are – integration and derivation respectively. When it comes to finding out the function of some integrals, you can avoid the hassle of doing the calculation and simply obtain the result with the help of an online integral calculator.
Get to know the concepts
Before you can proceed with the task of using an online integral calculator, you need to get the concepts cleared out first. The set of both irrational and rational numbers is called real numbers. Rational numbers can be expressed in the form p/q where p and q is prime to each other and q is a positive integer while q can be a positive or negative integer or zero. When a number represented in this way has a decimal form which is not non terminating or non-recurring, the number is called a rational number. All real numbers which are not rational numbers are called irrational numbers. Real numbers can be represented graphically on a line called the real number line, which extends to either side of the zero(which is at the centre of the line), to represent negative and positive numbers. Any number which does not fall on the real number line is called an imaginary number. An example of an imaginary number is which is frequently denoted by or. A function maps one or more numbers to another number. The set of number which is supplied or provided to a function is called the input. The input is the independent quantity in the function as we can select its value arbitrarily. The result of the mapping is called the output. The output is the dependent quantity as its value is determined by the input. It is this output that can be calculated with the help of an online integral calculator. An example of a function would be the remote control used to control the television. We insert the channel number through the remote and we view the corresponding channel as the output.
You have to understand functions if you want to effectively use an online integral calculator. Functions can take both real and imaginary numbers as input. The output is usually shown by the symbol where signifies the input. The output is usually denoted by . We would often like to know how the value of the output changes with respect to very small changes in the value of the input . The process of finding out the relationship between these changes is called differentiation. Differentiation is always with respect to another quantity, as we wish to know the change of the output when the input is changed by a small amount. Knowing such small changes will help us to make decisions based on the observations. For example, if we wish to know how fast a car is moving, we need to know how much distance the car is traversing in a very small amount of time. This will help to determine the speed of the car, which in turn will help us to decide whether the car should be slowed down or accelerated. In our daily life, this particular instance of manipulating the speed of the car is an intuitive process, built over time through experience, but, in other cases we may not be physically present to take such decisions intuitively, such as manipulating a drone. In these cases we have to work on the data provided and take an action. Differentiation is an important tool to work with, for these cases. The process of differentiation often leads to a resulting function which is different from its parent function. For example, given a function , and differentiation with respect to , we get . Here denotes a small change in with respect to a small change in and is called the derivative of . This value of can be represented by a another function where, . Hence, if the value of is increased by 1, the corresponding increase in the value of , will be by 2.There are situations when the function is known to us and we would like to find the function . The process of doing so is called integration and the desired function, is called the integral. Keep this concept in mind when you are using an online integral calculator. Integration deals with different types of integrals, some of which are, indefinite integrals, definite integrals, double integrals and improper integrals. Integration often helps in calculating the area bounded by a curve. When a function is represented graphically, it should be continuous, or without breaks, in order to be differentiable or integrable. Often functions tend to represent a curve and it is useful to find how much area is present under the curve and the co-ordinate axes. These measurements are important for scientific applications. In such situations, definite integrals are very useful. Definite integrals utilize the concept of an interval, where the value of the input, is restricted to a particular range. So, if we have a function , and we integrate for , the integral is and the area under the curve is 3 units. As the integral and derivate are inverse to one another the integral is often called the anti-derivative.
How to use an online integral calculator
An online integral calculator will get the calculation done for you so that you do not have to do it manually and you can get the correct result. All that you will have to do is enter the function that you wish to integrate, in lieu of which a graphical representation will be shown to you. Check whether you get the right graphical presentation or not and then request for the specified function that you want. Which functions are performed by the integral calculator will be provided in the calculator itself and you will have to specify the limits of the function, or else only the anti-derivate part of a function will be calculated.
Image Credits: Math and Multimedia
Also check out our article on 6 Tricks for Faster Calculations here.