Anti Derivative

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Derivatives and anti-derivatives are the two important methods used to solve questions in Calculus. Anti-derivative is the process of finding the area covered below the graph of the given function. Anti-derivative is the opposite of the derivative process and is commonly known as the process of Integration.

Example 1: Find the anti-derivative of the function, f(x) = x3- 2x

In order to find the anti-derivative of the above function, we can use the formula

The Power Rule of Integration says that ∫ (x) n dx = x (n+1)/ (n+1) + c

where ‘c’ is a constant

Using the above formula we get,

∫ f(x) dx = x3+1/ (3+1) - 2x1+1/ (1+1)+ c
∫ f(x) dx = x4/ 4 - 2 x2/ (2)+ c
∫ f(x) dx = x4/4 – x2 + c

Example 2: Find the anti-derivative of the function, f(x) = 5x4 + 4x3 – x-2

In order to find the anti-derivative of the above function, we can use the formula:

The Power Rule of Integration says that ∫ (x) n dx = x (n+1)/ (n+1) + c
where ‘c’ is a constant

Using the above formula we get,
∫ f(x) dx = 5 * x4+1/ (4 +1) + 4 * x3+1/ (3 +1) –  x-2+1/ (-2+1) + c
∫ f(x) dx = 5 * x5/ 5 + 4 * x4/ (4) – x-1/(-1) + c
∫ f(x) dx = x5 + x4 + 1/x + c