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Improper Integral Calculator

Evaluate improper integrals with infinite bounds or discontinuities, with a convergence verdict.

Related tools

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Improper Integral Calculator works straight from this page — free, instant, nothing to install. It sits under Calculus in our catalogue, alongside Double Integral Calculator and Exponential Integral Calculator.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Improper Integral Calculator?

Evaluate improper integrals with infinite bounds or discontinuities, with a convergence verdict.

When would I actually use this?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

How is Improper Integral Calculator different from Double Integral Calculator?

They sit next to each other but answer different questions: Double Integral Calculator is the one to open when you need it to numerically evaluate a double integral ∬ f(x,y) over a rectangular region. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Exponential Integral Calculator is the closest one after this: Compute the exponential integral Ei(x) for any real x ≠ 0 to a chosen precision, using the convergent series γ + ln|x| + Σ xᵏ/(k·k!) or the asymptotic series for large arguments.

What else is worth having open alongside it?

Line Integral Calculator and Surface Integral Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

Further reading

All guides →
ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.