Antiderivative calculator - Step by step calculation
Antiderivative calculator finds the antiderivative of a function step by step with respect to a variable i.e., x, y, or z. This online integration calculator also supports upper bound and lower bound in case you are working with minimum or maximum value of intervals.
With this integral calculator, you can get step by step calculations of:
- Definite integral
- Indefinite integral
It can find the integrals of logarithmic as well as trigonometric functions. This tool assesses the input function and uses integral rules accordingly to evaluate the integrals for the area, volume, etc.
How does antiderivative calculator work?
This tool uses a parser that analyzes the given function and converts it into a tree. The computer interprets the tree to correctly evaluate the order of operations and implements the integration rules appropriately.
You can find the antiderivative (integral) of any functions by following the steps below.
- Select the definite or indefinite option.
- Enter the function in the given input box.
- Click the Load Example button if you want to use a sample example.
- Specify the variable. It is set as x by default.
- Enter the Upper and Lower bound limit if you chose definite integral above.
- Hit the Calculate button. You will get the result with step-by-step calculations.
You can download the solution by clicking on icon.
What is an Integral?
An integral can be defined as,
“Integral assigns numbers to functions in a way that describes volume, area, displacement, and other ideas that arise by combining infinitesimal data.”
The process of finding integrals is called integration. Integral is also referred to as antiderivative because it is a reverse operation of derivation.
Along with differentiation, integration is an essential operation of calculus and serves as a tool to solve problems in mathematics and physics involving the length of a curve, the volume of a solid, and the area of an arbitrary shape among others.
The integral of a function f(x) with respect to a real variable x on an interval [a, b] is written as:
How to find Antiderivative (Integral)?
See the below examples to learn how to evaluate definite and indefinite integrals using rules of integration.
Example # 1
- Apply the sum rule. Write integration sign with each variable separately.
The above function can be written as:
- Apply power rule on both expressions to evaluate the exponents.
- Apply constant rule which leave C with the final expression.
Example # 2
- Rearrange the function as below.
- Apply sum rule to the function.
|------ Equ. 1|
- Solve each expression in the above function by implementing integral rules.
|------- d/dx sin(x) = cos(x)|
|------- Power rule applied.|
|------- Power rule applied. Refer to previous example|
- Substitute the solve values in Equation 1.
C is added because of the constant rule.
- Simplify the equation if needed.
What is the integral of 1/x?
The integral of 1/x is an absolute value: ln (|x|) + C. It is a standard integration value.
What is the difference between definite and indefinite integral?
A definite integral denotes a number when the upper and lower bounds are constants. On the other hand, the indefinite integral is a family of functions whose derivatives are f. The difference between the two functions is a constant.
What is the antiderivative of tan(x) dx?
The antiderivative of tan(x) dx is,
tan x = - ln |cos x| + C