Anti Derivative

Anti Derivative The method of finding the Antiderivative of a function is also known as the method of Integration. There are two types of antiderivatives, one being the indefinite integrals where the constant c is includedin the answer of the function. The other type of antiderivatives is the definite integrals where the constant c is not included and the final solution of the antiderivative is computed by substitution of numbers. Example 1: Find the anti-derivative of the function, f(x) = 8x3- 10x + 9 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 = 8 * x3+1/ (3+1) 10 * x1+1/ (1+1) + 9x + c f(x) dx = 8 * x4/ 4 10 * x2/ (2) + 9x + c f(x) dx = 2x4 5x2 + 9x + c Example 2: Find the antiderivative of the definite integral value of the function, f(x) = 3x2 + 2x and x ranging from 0 to 2. xn dx= x(n+1)/ (n+1) Apply the above formula for the given function, we get (fx) dx = 3* x2+1/(2 + 1) + 2*x1+1/(1 + 1) f(x)dx = x3 + x2 First substitute x =0 and x= 2 in the above answer. When x=0, f(x) dx= 03 +02= 0 When x=2, f(x)dx= 23 + 22 = 12 Now subtract 12 - 0 = 12 Hence the antiderivative of given f(x) is 12.