Math

Find the Integral

How to Find the Integral of Any Function

Finding an integral tells you the total accumulation of a quantity. Enter your function below and this calculator will find the integral for you using high-precision numerical methods. No sign-up required.

Integral Calculator Tips

Click to show tips

Try an Example

Pick a scenario to see how the calculator works, then adjust the values

Basic Polynomial

Integrate x^2 from 0 to 1 using Simpson's rule. Exact answer: 1/3.

Key values: x^2 · [0, 1] · Simpson's rule

Trigonometric Integral

Integrate sin(x) from 0 to pi. Exact answer: 2.

Key values: sin(x) · [0, pi] · Exact: 2

Area Under a Bell Curve

Approximate the Gaussian integral e^(-x^2) from -3 to 3.

Key values: e^(-x^2) · [-3, 3] · Gaussian

Documentation

This calculator is also known as Find the Integral.

Read the complete guide

What Is an Integral?

An integral measures the total accumulation of a quantity. If velocity is v(t), the integral gives total distance. If rate of flow is r(t), the integral gives total volume. It's the area under the curve.

Quick Guide

Steps to find an integral:

Enter the function f(x) in the input field
Set the lower bound a and upper bound b
Click Calculate to get the result
Use the Riemann slider to visualize the approximation

Examples

Finding the Integral of x^2

Find the integral of x^2 from 0 to 1.

The integral equals 1/3 = 0.3333.

Key takeaway: Start with simple polynomials to build your understanding.

Tips for Finding Integrals

Use these tips to find integrals effectively:

Start by entering a simple function like x^2 to see how it works
Pay attention to the sign of the result -- negative means the curve is below the x-axis
Use the Riemann rectangle slider to build geometric intuition

Frequently Asked Questions about Find the Integral

How do I find an integral step by step?

Enter your function, set bounds, and click Calculate. The calculator uses high-precision numerical methods. For manual practice: (1) find an antiderivative F(x), (2) evaluate F(b) - F(a). If no antiderivative exists, numerical methods are the way to go.

Specialized Calculators

Choose from 7 specialized versions of this calculator, each optimized for specific use cases and calculation methods.

Purpose

3 Calculators

Definite Integral

Definite Integral Calculator | Evaluate Definite Integrals

Calculate the exact value of any definite integral with step-by-step solutions and shaded area visualization.

definiteevaluatebounds

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Area Under Curve

Area Under Curve Calculator | Shaded Area Visualization

Calculate the area under any curve between two x-values with a shaded visualization showing positive and negative regions.

areacurveshaded+1

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Numerical Integration

Numerical Integration Calculator | Compare Methods

Compare Simpson's rule, trapezoidal rule, and midpoint rule for numerical integration with method comparison.

numericalcomparisonmethods+1

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Method

4 Calculators

Alternative methods and approaches

Simpson's Rule Calculator | Numerical Integration

Apply Simpson's 1/3 rule to approximate definite integrals with error analysis and step-by-step solution.

simpsonsnumericalquadrature

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Trapezoidal Rule

Trapezoidal Rule Calculator | Trapezoid Approximation

Use the trapezoidal rule to approximate integrals with trapezoid visualization and error analysis.

trapezoidaltrapezoidnumerical

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Riemann Sum Calculator | Interactive Rectangle Visualization

Compute midpoint Riemann sum approximations with an interactive rectangle visualization and n slider.

riemannrectanglemidpoint+1

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Midpoint Rule Calculator | Integration Approximation

Apply the midpoint rule to approximate definite integrals. Ideal when the function is undefined at endpoints.

midpointnumericalendpoint-singularity

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