Antiderivative of X

Antiderivative of X Anti-derivatives is the reverse or opposite of derivatives. Here the function given is x and the exponent to which the variable is raised is 1. The power rule is used to find the anti-derivative for any function which contains a variable raised to an exponent.According to the power rule any function which has the variable raised to the power n is written as xn has theanti-derivative = xn dx= x(n+1)/ (n+1) + c.Hence the anti- derivative of the function x is 1x2/2. Example 1: Find the anti-derivative of the function f(x) = x + 6x3 Here the given function is f(x) = x + 6x3 The anti-derivative of x is 1/2 * x2 Using the power rule, the anti-derivative of 6x3 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 6x3 is 6x4/4. Hence F(x) = 1x2/2 + 3x4/2 + c Example 2: Find the anti-derivative of the function f(x) = 15 x. Here the given function is f(x) = 15 - 3x. The anti-derivative of x is 1/2 x2 Using the power rule, the anti-derivative of 15 has to be found. Power rule states that anti-derivative of xn = xn dx= x(n+1)/ (n+1) + c 15 can be written as 15 x0. Therefore, the anti-derivative of 15 x0 is 15x1 Hence F(x) = 15 x -x2/2 + c