# Improper Integral Calculator

The improper integral is the reversing of the process of differentiation. An improper integral is an integral which have an upper limit and a lower limit. The improper integral also find the area under the curve from the lower limit to the upper limit. Improper integral is also known as a definite integral.

## What is an Improper Integral Calculator?

An 'Improper Integral Calculator' is a free online tool that helps to calculate the improper integral value for a given function. In this calculator, you can enter the function, upper, and lower limit and the value of improper integral will be displayed within a few seconds.

## How to Use Improper Integral Calculator?

Follow the steps given below to use the calculator:

**Step 1:**Enter the function, upper and lower limit in the space provided.**Step 2:**Click on**"Calculate"**.**Step 3:**Click on**"Reset"**to clear the field and enter new values.

## How to Find an Improper Integral?

Integration is defined as the reverse process of differentiation. The integration is represented by** ' ∫ '**. Improper integrals are integrals that have upper and lower limits. It is represented as ^{b}∫_{a}f(x)dx. The fundamental theorem of calculus tells us that to calculate the area under a curve y = f(x) from x = a to x = b, we first calculate the integration g(x) of f(x),

**g(x) = ∫ f(x) dx**

And then evaluate g(b) − g(a). That is, the area under the curve f(x) from x=a to x=b is

^{b}∫_{a }f(x) dx = g(a) - g(b)

There are common functions and rules we follow to find the integration.

**Solved Example:**

Find the integration of value ^{9}∫_{6}** **(2x - 7) dx

**Solution:**

^{9}∫_{6} (2x - 7) dx

= ^{9}∫_{6 }2x dx - ^{9}∫_{6 }7 dx

= x^{2} _{6}]^{9} - 7x _{6}]^{9}

= (9^{2} - 6^{2}) - 7(9 - 6)

= (81 - 36) - 7(3)

= 45 - 21

= 24

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