Integral Calculator with Work

This integral calculator solves definite and indefinite integrals with detailed step-by-step work. It provides visual graphing of the function and its integral, helping you understand the relationship between the original function and its antiderivative.

How to Use This Calculator

To solve an integral using this calculator:

Enter the function you want to integrate in the "Function" field. Use standard mathematical notation (e.g., x^2, sin(x), e^x).
For definite integrals, enter the lower and upper limits in the "Lower limit" and "Upper limit" fields.
Click "Calculate" to see the result and step-by-step work.
Review the graph visualization to understand the relationship between the original function and its integral.

The calculator will display:

The integral result
Step-by-step work showing each integration rule applied
A graph of the original function and its integral

Formula Explained

The integral calculator uses standard integration techniques including:

Basic integration rules (power rule, constant rule, etc.)
Substitution method
Integration by parts
Trigonometric integrals
Exponential and logarithmic integrals

Basic Integration Rules

For a function f(x) = x^n, the integral is:

∫x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1

For the constant function f(x) = k, the integral is:

∫k dx = kx + C

The calculator automatically applies these rules and more complex techniques as needed to solve the integral.

Worked Examples

Example 1: Basic Power Function

Find the integral of f(x) = x^3.

Using the power rule:

∫x^3 dx = (x^(3+1))/(3+1) + C = x^4/4 + C

Example 2: Definite Integral

Find the definite integral of f(x) = x^2 from 0 to 1.

First find the antiderivative:

∫x^2 dx = x^3/3 + C

Then evaluate from 0 to 1:

[1^3/3] - [0^3/3] = 1/3 - 0 = 1/3

Example 3: Trigonometric Function

Find the integral of f(x) = cos(x).

The integral of cos(x) is:

∫cos(x) dx = sin(x) + C

Frequently Asked Questions

What types of integrals can this calculator solve? +

This calculator can solve both definite and indefinite integrals for a wide range of functions including polynomial, trigonometric, exponential, and logarithmic functions.

How accurate are the step-by-step solutions? +

The step-by-step solutions follow standard integration techniques and are verified for correctness. However, complex integrals may require additional verification.

Can I use this calculator for homework or exams? +

Yes, this calculator can be a helpful study tool. However, always verify your understanding of the integration techniques used.