How to Use the Integral Calculator
Whether you are verifying your homework, studying for a calculus exam, or solving advanced physics problems, finding the exact antiderivative of a function can be incredibly complex. Our Integral Calculator brings the power of a Wolfram Alpha style symbolic integration engine directly to your web browser.
This tool supports standard polynomial, exponential, logarithmic, and trigonometric functions. If you need to estimate the area under a curve numerically rather than symbolically, be sure to use our Riemann Sum Calculator. For other disciplines, explore all our Math Calculators.
Indefinite vs. Definite Integrals
Understanding the distinction between these two forms of integration is the cornerstone of calculus:
- Indefinite Integrals: Also known as an antiderivative, calculating an indefinite integral gives you a general function, $F(x)$. Because the derivative of any constant is zero, we must always add "$+ C$" (the constant of integration) to the end of our result.
- Definite Integrals: When we apply a lower bound ($a$) and an upper bound ($b$) to the integral, we are calculating the exact, finite area under the curve between those two points. The result is a specific number, not a general function.
Input Syntax Guide
To ensure the calculation engine understands your function, use standard mathematical syntax:
- Exponents: Use the caret symbol `^`. (e.g., `x^3`)
- Multiplication: Explicitly declare multiplication using an asterisk `*` when placing variables next to functions. (e.g., `x*sin(x)` instead of `xsin(x)`)
- Fractions: Use parenthesis to ensure the correct order of operations. (e.g., `1/(x+1)`)
- Constants: You can type `pi` for $\pi$ and `e` for Euler's number.