- Books Name
- Mathmatics Book Based on NCERT
- Publication
- KRISHNA PUBLICATIONS
- Course
- CBSE Class 12
- Subject
- Mathmatics
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.