Improper Integral Calculator

Evaluate improper integrals with infinite limits and discontinuities instantly

Calculate Improper Integral

Understanding Improper Integrals

An improper integral is a definite integral that has either:

  • An infinite limit of integration (e.g., ∫[0 to ∞] e^(-x) dx)
  • A discontinuity in the integrand (e.g., ∫[0 to 1] 1/x dx)

Our improper integral calculator handles both types by using advanced numerical methods to evaluate these challenging integrals accurately.

Frequently Asked Questions

What is an improper integral calculator?

An improper integral calculator is a tool that evaluates definite integrals with infinite limits or discontinuities in the integrand, which cannot be computed using standard integration techniques.

How accurate is this calculator?

This calculator uses Simpson's Rule with a high number of subdivisions to provide accurate results up to 6 decimal places for most well-behaved functions.

What types of functions can I integrate?

You can integrate various functions including polynomials, exponentials, trigonometric functions, and their combinations. Supported operations include +, -, *, /, ^, sqrt(), exp(), ln(), sin(), cos(), and tan().

How do I enter infinite limits?

Use the symbol ∞ for positive infinity and -∞ for negative infinity. You can copy these symbols or type "inf" for ∞.

Quick Guide

Example Functions

  • 1/x (reciprocal)
  • e^(-x) (exponential decay)
  • 1/x^2 (inverse square)
  • sin(x)/x (sinc function)

Common Limits

  • [0 to ∞]
  • [-∞ to ∞]
  • [1 to ∞]

Tips

  • Use parentheses to group operations
  • Check for typos if you get errors
  • Some improper integrals may diverge