Indefinite Integration-Topics in IB Mathematics

Indefinite Integration

After a long series on differentiation and ‘Application of derivatives‘, we shall now discuss Indefinite Integration. It consists of two different words indefinite and integration.
First of all, we shall learn about Integration.

 Integration is the reverse process of differentiation so we can also call it as antiderivative. There is one more name for it, that is Primitive.
If f & g are functions of x such that g'(x) = f(x) then the function g is called a Primitive Or Antiderivative Or Integral of  f(x) w.r.t. x and is written symbolically as:-

\int {f\left( x \right){\rm{ }}dx = g\left( x \right) + c}

If    \frac{d}{{dx}}\left\{ {f(x) + c} \right\} = f'(x)

then  \int {f'\left( x \right){\rm{ }}dx = f\left( x \right) + c}      here c is just an arbitrary constant. Value of c is not definite that’s why we call it Indefinite Integration.

Techniques  Of  Integration-: There are a few important techniques used to solve problems based on integration

(i) Substitution or  Change of Independent Variable- If the derivative of a function is given in the question, then we should use the method of substitution to integrate that question. Read more