`\color{green} ✍️` Integration is the inverse process of differentiation.
`\color{green} ✍️` Instead of differentiating a function, we are given the derivative of a function and asked to find its primitive, i.e., the original function. Such a process is called integration or anti differentiation.
`\color{green} ✍️` If there is a function F such that `d/(dx) F(x) = f(x) , AA x ∈ I` (interval), then for any arbitrary real number C, (also called constant of integration)
`color{orange}{d/(dx) [F(x) +C ] = f(x) , x ∈ I"`
`\color{green} ✍️` A new symbol, namely, ∫ f (x) dx which will represent the entire class of"`
`\color{green}" anti derivatives read as the indefinite integral of f with respect to x
Symbolically, we write `color{orange} (∫ f (x) dx = F (x) + C.)`
Notation Given that ` (dy)/(dx)= f(x)` , we write `y = ∫ f (x) dx .`
- we mention below the following symbols/terms/phrases with their meanings as given in the Table.
`\color{green} ✍️` Integration is the inverse process of differentiation.
`\color{green} ✍️` Instead of differentiating a function, we are given the derivative of a function and asked to find its primitive, i.e., the original function. Such a process is called integration or anti differentiation.
`\color{green} ✍️` If there is a function F such that `d/(dx) F(x) = f(x) , AA x ∈ I` (interval), then for any arbitrary real number C, (also called constant of integration)
`color{orange}{d/(dx) [F(x) +C ] = f(x) , x ∈ I"`
`\color{green} ✍️` A new symbol, namely, ∫ f (x) dx which will represent the entire class of"`
`\color{green}" anti derivatives read as the indefinite integral of f with respect to x
Symbolically, we write `color{orange} (∫ f (x) dx = F (x) + C.)`
Notation Given that ` (dy)/(dx)= f(x)` , we write `y = ∫ f (x) dx .`
- we mention below the following symbols/terms/phrases with their meanings as given in the Table.