Integral Calculator Online
Integral Calculator Online: Calculate Integrals Easily
Introduction
An Integral Calculator is a powerful online tool that helps students, teachers, engineers, and professionals solve integration problems step by step. Whether you are working with basic polynomials or complex trigonometric and exponential functions, this tool simplifies the process by instantly computing both indefinite integrals (general formula with constant of integration) and definite integrals (exact values over a given interval).
If you’ve ever struggled with calculus, an integral calculator online can save you time, reduce errors, and help you understand the logic behind the solution.
Formula / Working
In mathematics, integration is the reverse process of differentiation. The general formula is: ∫f(x) dx=F(x)+C\int f(x) \, dx = F(x) + C∫f(x)dx=F(x)+C
Where:
- f(x)f(x)f(x) = the function to be integrated
- F(x)F(x)F(x) = the antiderivative of f(x)f(x)f(x)
- CCC = constant of integration
For definite integrals, the formula is: ∫abf(x) dx=F(b)−F(a)\int_a^b f(x) \, dx = F(b) – F(a)∫abf(x)dx=F(b)−F(a)
Where:
- aaa = lower limit
- bbb = upper limit
The calculator uses built-in symbolic computation methods to quickly evaluate both definite and indefinite integrals.
Step-by-Step Usage
Using the online Integral Calculator is simple and requires no advanced knowledge:
- Enter the function you want to integrate (e.g.,
x^2,sin(x),e^x). - Choose whether you want an indefinite integral or input limits for a definite integral.
- Click the Calculate button.
- View the step-by-step solution with the final result.
- Use the Clear button to reset and calculate a new function.
Examples
Example 1: Indefinite Integral
∫x2dx\int x^2 dx∫x2dx
Solution: F(x)=x33+CF(x) = \frac{x^3}{3} + CF(x)=3×3+C
The calculator provides the result instantly.
Example 2: Definite Integral
∫02(2x)dx\int_0^2 (2x) dx∫02(2x)dx
Solution: F(x)=x2F(x) = x^2F(x)=x2 F(2)−F(0)=(22)−(02)=4F(2) – F(0) = (2^2) – (0^2) = 4F(2)−F(0)=(22)−(02)=4
So, the definite integral from 0 to 2 equals 4.
Example 3: Trigonometric Integral
∫sin(x)dx\int \sin(x) dx∫sin(x)dx
Solution: F(x)=−cos(x)+CF(x) = -\cos(x) + CF(x)=−cos(x)+C
FAQs
1. What is an Integral Calculator?
It’s an online tool that solves integration problems automatically, giving quick solutions for both definite and indefinite integrals.
2. Who can use this tool?
Students, teachers, engineers, researchers, and anyone working with calculus can benefit from it.
3. Does the calculator show steps?
Yes, it provides step-by-step explanations for better learning.
4. Can it solve definite integrals with limits?
Yes, simply enter the upper and lower limits, and the tool will compute the exact value.
5. Is this tool free to use?
Yes, most online integral calculators are completely free and accessible anytime.