Antiderivative Calculator

What is an Antiderivative?

An antiderivative, also known as an indefinite integral, is a function whose derivative is the given function. In other words, if F(x) is an antiderivative of f(x), then F’(x) = f(x). The process of finding antiderivatives is called integration.

How to Use the Antiderivative Calculator

1. Enter the function you want to integrate in the input field.
2. Click the “Calculate” button.
3. The calculator will display the antiderivative of your function.

For example, if you enter “x^2”, the calculator will return “x^3/3 + C”, where C is the constant of integration.

Understanding the Results

The antiderivative is always expressed with “+ C” at the end. This constant of integration represents the fact that there are infinitely many antiderivatives for any given function, differing only by a constant.

Common Antiderivative Rules

Here are some basic antiderivative rules to help you understand the process:

1. Power Rule: ∫ x^n dx = (x^(n+1))/(n+1) + C (where n ≠ -1)
2. Exponential Rule: ∫ e^x dx = e^x + C
3. Trigonometric Rules:
   • ∫ sin(x) dx = -cos(x) + C
   • ∫ cos(x) dx = sin(x) + C
   • ∫ tan(x) dx = -ln|cos(x)| + C

Applications of Antiderivatives

Antiderivatives have numerous applications in physics, engineering, and economics:

1. Finding displacement from velocity in physics
2. Calculating work done by a variable force
3. Computing probability distributions in statistics
4. Analyzing economic growth models

Tips for Using the Antiderivative Calculator

1. Always simplify your function before entering it into the calculator.
2. Use parentheses to group terms correctly.
3. For trigonometric functions, use “sin”, “cos”, “tan”, etc.
4. For exponentials, use “e^x” or “exp(x)”.

Ready to solve your integration problems? Try our antiderivative calculator now and make your calculus tasks a breeze!

Frequently Asked Questions

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