About Integral Calculator
This integral calculator computes definite integrals numerically using Simpson's rule, one of the most accurate numerical integration methods. Simply enter your function f(x), the lower bound a, the upper bound b, and the number of subintervals n (higher values yield greater accuracy). The calculator evaluates the function at multiple points within the interval and applies Simpson's composite rule to approximate the area under the curve. Results include the numerical value, bounds, method details, and estimated error. This tool is essential for calculus students verifying analytic solutions, engineers performing quick calculations, and scientists analyzing accumulated quantities. The step-by-step breakdown shows the formula application for educational understanding.
Frequently Asked Questions
What is the Integral Calculator?
The Integral Calculator computes definite integrals numerically using Simpson's rule. It approximates the area under a curve f(x) between lower bound a and upper bound b, with step-by-step output.
How accurate is the numerical integration?
Accuracy depends on the number of subintervals (n). Higher n values produce more accurate results. Simpson's rule has error proportional to 1/n^4, making it very efficient for smooth functions. Use n=1000 or more for high precision.
What functions does the Integral Calculator support?
It supports standard mathematical functions including sin(), cos(), tan(), log(), ln(), sqrt(), abs(), exp(), and exponentiation (^). Use standard algebraic notation like x^2, 2*x+3, or sin(x)+cos(x).
Is the Integral Calculator free?
Yes, the Integral Calculator is completely free to use with no registration or limits.