Integral Calculator Derivative

This integral calculator and derivative calculator provides step-by-step solutions for calculus problems. Whether you're solving definite integrals, indefinite integrals, or derivatives, our tool helps you understand the process and verify your results.

What is an Integral Calculator?

An integral calculator is an online tool that computes integrals (both definite and indefinite) for various functions. It's particularly useful for students, engineers, and anyone working with calculus problems. Our integral calculator supports a wide range of functions, including polynomial, trigonometric, exponential, and logarithmic functions.

The calculator provides step-by-step solutions, helping you understand how the integral was computed. This is especially valuable for learning purposes, as it allows you to see the intermediate steps and verify your manual calculations.

How to Use an Integral Calculator

Using our integral calculator is straightforward. Follow these steps:

Enter the function you want to integrate in the input field.
Select whether you want to compute a definite or indefinite integral.
If you're computing a definite integral, enter the lower and upper limits.
Click the "Calculate" button to get the result.

The calculator will display the result along with a detailed solution showing each step of the integration process.

Derivative Calculator

In addition to integral calculations, our tool also includes a derivative calculator. This feature computes the derivative of a given function. The derivative calculator is useful for finding rates of change, slopes of tangent lines, and solving differential equations.

Like the integral calculator, the derivative calculator provides step-by-step solutions to help you understand the process. This is particularly helpful for students learning calculus concepts.

Formulas

Integral Formulas

Indefinite Integral: ∫f(x) dx = F(x) + C

Definite Integral: ∫[a to b] f(x) dx = F(b) - F(a)

Power Rule: ∫x^n dx = (x^(n+1))/(n+1) + C (n ≠ -1)

Exponential Rule: ∫e^x dx = e^x + C

Derivative Formulas

Power Rule: d/dx [x^n] = n*x^(n-1)

Exponential Rule: d/dx [e^x] = e^x

Logarithmic Rule: d/dx [ln(x)] = 1/x

Examples

Integral Example

Compute the definite integral of x² from 0 to 2.

Using the power rule: ∫[0 to 2] x² dx = (x³/3) evaluated from 0 to 2 = (8/3) - 0 = 8/3 ≈ 2.6667

Derivative Example

Find the derivative of 3x³ + 2x - 5.

Using the power rule: d/dx [3x³ + 2x - 5] = 9x² + 2

FAQ

What types of integrals can I calculate?

Our integral calculator supports definite and indefinite integrals for polynomial, trigonometric, exponential, and logarithmic functions.

How accurate are the results?

The calculator uses standard calculus formulas and provides step-by-step solutions to ensure accuracy. For complex functions, results may be approximate.

Can I use this calculator for homework?

Yes, our calculator is designed to help with homework and learning calculus. The step-by-step solutions make it an excellent learning tool.