Basic Integral Calculator

This basic integral calculator helps you compute definite and indefinite integrals of common functions. Whether you're a student studying calculus or a professional needing quick calculations, this tool provides accurate results with step-by-step explanations.

What is an Integral?

An integral represents the area under a curve between two points. It can be calculated as a definite integral (with limits) or an indefinite integral (antiderivative). Integrals are fundamental in calculus and have applications in physics, engineering, economics, and more.

There are two main types of integrals:

Definite Integral: Calculates the exact area under a curve between two specified limits.
Indefinite Integral: Finds the antiderivative of a function, which represents the family of functions whose derivative is the original function.

How to Use This Calculator

Using our basic integral calculator is simple:

Select the type of integral you want to calculate (definite or indefinite).
Enter the function you want to integrate.
For definite integrals, specify the lower and upper limits.
Click "Calculate" to get the result.
Review the step-by-step solution and graph visualization if available.

Tip: For complex functions, use proper mathematical notation. For example, enter "x^2" as x^2 or x**2, not x2.

Basic Integral Formulas

Here are some common integral formulas:

∫x^n dx = (x^(n+1))/(n+1) + C (for n ≠ -1) ∫e^x dx = e^x + C ∫a^x dx = (a^x)/ln(a) + C (for a > 0, a ≠ 1) ∫sin(x) dx = -cos(x) + C ∫cos(x) dx = sin(x) + C ∫sec²(x) dx = tan(x) + C ∫csc(x)cot(x) dx = -csc(x) + C ∫sec(x)tan(x) dx = sec(x) + C

Where C is the constant of integration for indefinite integrals.

Example Calculations

Let's look at a few example calculations:

Example 1: Definite Integral

Calculate ∫ from 0 to 1 of x^2 dx:

∫x^2 dx = (x^3)/3 evaluated from 0 to 1 = (1^3)/3 - (0^3)/3 = 1/3 - 0 = 1/3 ≈ 0.3333

Example 2: Indefinite Integral

Find the antiderivative of x^3:

∫x^3 dx = (x^4)/4 + C

Example 3: Trigonometric Integral

Calculate ∫ from 0 to π/2 of sin(x) dx:

∫sin(x) dx = -cos(x) evaluated from 0 to π/2 = -cos(π/2) - (-cos(0)) = -0 - (-1) = 1

Frequently Asked Questions

What types of integrals can this calculator solve?: This calculator can solve both definite and indefinite integrals of common functions, including polynomials, exponential functions, and trigonometric functions.
How accurate are the results?: The calculator uses standard integral formulas and provides exact results for basic functions. For complex functions, results may be approximate.
Can I integrate functions with variables other than x?: Currently, the calculator is optimized for functions with the variable x. Support for other variables may be added in future updates.
Is there a mobile app version of this calculator?: We don't have a dedicated mobile app, but our web calculator works well on all devices, including smartphones and tablets.
How can I learn more about integrals?: For a deeper understanding of integrals, we recommend checking out our related calculators in the Math category and exploring calculus textbooks or online resources.