Find the Antiderivative

Find the Antiderivative Find the Antiderivative Antiderivative is reverse operation of derivation and definition suggest that if f(x) is function and derivative of f(x) is g(x) then antiderivative of g(x) is f(x):d (f(x)) = g(x) then antiderivative of g(x) means integration of g(x) is âˆŤg(x) dx = f(x) + c dx For finding antiderivative of functions we use several steps they are as follows:Step 1: First of all judge function which antiderivative we want to calculate means judge the function's derivative by using integration operation.

Like we want to calculate antiderivative of f(x) = 2x, then first of all we calculate integration operation on 2x: âˆŤ2x dx = 2.x2 + c = x2 + c.

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2 Step 2: After integration operation on function, we put 0 as a constant value like we get x2 + c in above example, then we put c = 0 and produce x2 as a result of antiderivation.

So, these two steps we use for finding the antiderivative of particular function.

We take some example to understand the methodology of antiderivative.

Example 1: Find the antiderivative of cos x?

Solution :- Step 1: First of all we calculate integration of cos x – ∫cos x dx = sin x+c Step 2: in this step we put 0 as a constant value means we put c = 0, sin x + 0 = sin x So, antiderivative of cos x is sin x .

Example 2: Find the antiderivative of sin x ?

Solution :- Step 1: First of all we calculate integration of sin x, ∫sin x.dx = - cos x + c, Step 2: In this step we put o as a constant value c, - cos x + 0 = -cos x, So, antiderivative of sin x is -cos x.

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