Improper Integral Calculator



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Introduction to the Improper Integral Calculator

An improper integrals calculator is an online tool to evaluate the improper integral. Basically the integral convergence calculator is a definite integrals calculator that has infinite value in one or both limit values of integral. This online calculator displays the integrated values in a few seconds.

What is an Improper Integral Calculator with Steps

An improper integral convergence test calculator is an online tool designed to calculate improper integrals. This tool is also used to check the convergence and divergence of the given function. Both the convergence and the divergence of the function is evaluated using the converge or diverge calculator integral with possible intermediate steps and graphs.

Unlike to improper integral, if you want boundary less calculation of integration problem, you need to try our indefinite integration calculator for efficient and stepwise calculations.

Formula used by Improper Integral Solver

Improper integral convergence calculator uses the following formula to perform mathematical calculations on users provided function and data. The formula is as follow:

$$ \int_1^∞ F(x) dx $$

Note: The Area Under Curve Calculator is a special case of the "Improper Integral Calculator" as the area under a curve can be calculated using an improper integral, which can be evaluated using the "Improper Integral Calculator".

Let's see how to calculate improper integral in a stepwise method

Improper Integral Example:

Consider we have a function $$ \int_1^∞ \frac{1}{x} dx $$


$$ \int_1^∞ \frac{1}{x} dx \;=\; \lim \limits_{b \to ∞} \int_1^b \frac{1}{x} dx $$ $$ \;=\; \lim \limits_{b \to ∞} [ln x]_1^b $$ $$ \;=\; \lim \limits_{b \to ∞} [ln b - ln 1] $$

Moreover, you can also try our double integration calculator for taking the integral of already integrated function.

How does Improper Integral Convergence Calculator Work?

There are many ways to calculate improper integrals. The best among all these methods is below by using improper integrals calculator.

Following are the steps that we need to do while working on the convergent or divergent integral calculator:


  1. Write your function in the Required bar.
  2. Now, select the variable w.r.t which you want to find the integral online.
  3. Then, select your required limits for the process of integration.
  4. Then just do one click on "CALCULATE" button.


The improper integral calculator with steps will calculate the following factors:

  1. It calculates the definite or indefinite integrals.
  2. It applies limits to given functions to determine whether the integral is convergent or divergent.
  3. The convergent or divergent integral calculator shows step-by-step calculations which are carried out.

Related: If you need to calculate the volume under a three-dimensional surface, the triple integral solver can be a useful tool to simplify the process and get accurate results.

How to Find Converge or Diverge Calculator Integral?

To find the converge or diverge integral calculator for the integral calculation, just follow the following steps:

  • First of all, open the browser's home screen.
  • Now, enter the calculator keywords, that is improper integration calculator, definite improper integral solver or converge or diverge calculator in the search bar.
  • Now wait for the searched results.
  • Now select the Integral Calculator from Google suggestions.
  • Now click on the this integral convergence calculator for the evaluation of your problem. Now, simply add the values in the required fields to get the results.

Benefits of Improper Integral Convergence Test Calculator

The improper integrals calculator with steps has amazing benefits for its users. This online calculator gives you proper assistance in solving the improper integrals of the any function with stepwise results. The converge and diverge integral calculator is free of cost and is available online. It gives its users free services by providing accurate results.

The improper integrals calculator has the following benefits:

  • The improper integral solver is a time-saving tool.
  • It can evaluate the limits of the different given functions.
  • This improper integral calculator with steps can also be used to find the definite and indefinite imroper integrals.
  • The convergent or divergent calculator integral tool is reliable and easy to use calculator.
  • It gives you accurate results.
  • This tool is user-friendly among its users and calculate results in a seconds.

Frequently Asked Question

What is Improper Integral?

An improper integral is a type of integration that determines the area between a curve. This kind of integration has an upper limit and a lower limit. An improper integral can be considered a type of definite integral which can be solved by improper integral calculator.

Is 1/x an Improper Integral?

For finding an integral involving the function 1/x, look at the two common scenarios to calculate if the integral is improper,

  • While you consider the integral of 1/x on an interval that extends to infinity then the integral is improper because of the unbounded limits.
  • While you consider the integral of 1/x having a singularity in the range of integration the integral is improper because of the singularity. This type of integral also diverges due to the singularity.

Explain Why the Integral is Improper. 16 1 x dx 0

An integral is considered as an improper integral when there are unbounded limits of the integration which extends to infinity or negative infinity. When there are singularities in the integrand and the integrand has an undefined or infinite behavior within the limits of integrations.

The given integral is an improper integral because of the singularity. When the function has a singularity in the integration limits then the integration should be handled with care generally by using the limit-based approach which is also used by the divergent or convergent calculator.

How to Find the Convergence of Improper Integral

In some improper integrals, direct evaluation by integration and applying the limits can find the convergence, also used by the convergent divergent calculator. There is a comparison test that will compare the improper integral with the known convergent or divergent integral. There are two forms of the test
One is a direct comparison test in which if the f(x)≤g(x) for all the x in the integral and if the integral of g(x) converges then the integral of f(x) also converges. On the other hand, if the integral of g(x) diverges then the integral of f(x) also diverges.

If the limit is equal to c where c is a finite positive number then both integrals converge or both diverge.

For some functions that are decreasing and positive the integral test can help calculate convergence by comparing with known series results.

What Makes an Integral Improper

An integral is improper when there are one or more conditions that prevent to evaluate improper integral using standard methods. Such conditions involve infinite limits of integration or singularities in the integrand. Improper integrals need special handling involving limit-based techniques to get their divergence or convergence.

How to Determine if an Integral is Improper?

  • Find out whether one or both of the bounds is infinite.
  • Now find that one or both of the bounds are discontinuous on the function we are integrating.
  • If neither of the cases in Step 1 nor Step 2 occur, then the integral is proper.

What is the Difference Between an Improper Integral and a Proper Integral?

The main difference between proper and improper integral is that the proper integral has finite boundaries, while the improper integral has at least one infinite boundary.

Is the Gamma Function Improper Integral?

Yes, the improper integrals have a gamma (δ) function. The EULER’s integral 2nd kind is the type of the improper integral.