Antiderivative of 3x

Antiderivative of 3x Anti-derivatives is the reverse or opposite of derivatives. Here the function given is 3x therefore the powerrule is used to find the anti-derivative. According to the power rule any function which has the variable raisedto 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