2. Integration as an Inverse Process of Differentiation

Integration as an Inverse Process of Differentiation

Example : Find the anti derivative F of f defined by f (x) = 4x³ – 6, where F (0) = 3

Solution: One anti derivative of f (x) is x⁴ – 6x since

Therefore, the anti derivative F is given by

F(x) = x⁴ – 6x + C, where C is constant.

Given that F(0) = 3, which gives,

3 = 0 – 6 0 + C or C = 3

Hence, the required anti derivative is the unique function F defined by

F(x) = x⁴ – 6x + 3.