### Anti-Differentiation

#### Introduction to Anti-Differentiation

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###### Introduction to Anti-Differentiation | Video by ATAR Survival Guide

Anti-Differentiation could be phrased as 'reverse-differentiation' as it simply going the opposite way to differentiation. The above video goes through an introduction to differentiation.

###### What is Anti-Differentiation?

Anti-Differentiation could be phrased as 'reverse-differentiation' as it simply going the opposite way to differentiation. The above video goes through an introduction to differentiation.

The formula for Anti-Differentiation is provided above and is also in your formula sheet. Just remember, x cannot be a power of -1 as you cannot divide anything by 0.

###### Wait, What About C?

When we differentiate a constant, it is lost. As a result, when we do anti-differenitation, that constant can be anything, it can 0 all the way to infinity. As a result, we put the constant C to symbolise the possibilities of this number.

See below for an example.

**Important: Make sure you put the C, otherwise you might lose marks! **

###### Worked Example: Anti-Differentiation

In the above example, we have to differentiate the following equation:

**3x^4 + 6x^2 + 8**

The above steps highlight how we achieve the differentiated answer of **12x^3 + 12x**.

Notice how in the differentiation we lose the 8. This is important in the below where we anti-differentiate.

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As anti-differentiation is the reverse, let's anti-differnetiate our result from the previous step.

The goal here is to anti-differentiate the following equation:

**12x^3 + 12x**

By increase the power of x by +1 and dividing it by the new number, we get the following answer:

**3x^4 + 6x^2**

But wait? What about the constant? We have no evidence that it was 8 like the previous step, in a matter of fact it can be anything!

As such, we put the C to represent the constant - in other words, letting the person know this number can be anything!