Antiderivative of 3x

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Anti-derivatives is the reverse or opposite of derivatives. Here the function given is 3x therefore the power rule is used to find the anti-derivative. According to the power rule any function which has the variable raised to the power ‘n’ is written as ‘xn’ has the anti-derivative =∫xn dx= x(n+1)/ (n+1) + c. Hence the anti-derivative of :

‘3x’ is 3x2/2.


Example 1: Find the anti-derivative of the function f(x) = 3x + 4x2

Here the given function is f(x) = 3x + 4x2.

The anti-derivative of the function ‘3x’ is 3x2/2

Using the power rule, the anti-derivative of 4x2 has to be found.

Power rule states that anti-derivative of xn= ∫xn dx= x(n+1)/ (n+1) + c

Therefore, the anti-derivative of 4x2 is 4x3/3.

Hence the antiderivative of the given function is = 3x2/2 + 4x3/3 + c


Example 2: Find the anti-derivative of the function f(x) = 11 - 3x

Here the given function is f(x) = 11 - 3x.

The anti-derivative of the function ‘3x’ is 3x2/2

Using the power rule the anti-derivative of 11 needs to be found.

Power rule states anti-derivative of xn= ∫xn dx= x (n+1)/ (n+1) + c

11 can be written as 11 x0

Therefore, the anti-derivative of 11 x0 is 11x1

Hence antiderivative of the given function is = 11x – 3x2/2 + c


 

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