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# 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.

### Improper Integral Calculator

## 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

**\(\int_{a}^{b} f(x) dx = g(a) - g(b)\)**

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

**Solved Examples on Improper Integral Calculator**

**Example 1:**

Find the integration of value \(\int_{6}^{9} (2x - 7) dx\) and verify it using improper integral calculator.

**Solution:**

\(\int_{6}^{9} (2x - 7) dx\)

= \(\int_{6}^{9} 2x dx - \int_{6}^{9} 7 dx\)

= \(x^2|_6^9 - 7x|_6^9\)

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

= (81 - 36) - 7(3)

= 45 - 21

= 24

**Example 2:**

Find the integration of value \(\int_{2}^{3} (5x^{2}) dx\) and verify it using improper integral calculator.

**Solution:**

\(\int_{2}^{3} (5x^{2}) dx\)

= (5/3)\(x^3|_2^3\)

= 5/3(3^{3} - 2^{3})

= 5/3(27 - 8)

= 5/3(19)

= 95/3

= 31.666

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