Indefinite integral is the set of functions F(x) + C, where C is any real number and F(x) is the integral of f(x) whereas Integral is the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x). In other words Indefinite integral is anti derivative of the functions. It is written as ∫ f(x)dx (without upper and lower limits).
If ∫ f(x)dx = F + c
Where F is the anti derivative of f and C is the arbitrary constant
Here f is called as integrand and x is the variable of integration.
Indefinite Integral is so called because it’s value can’t be determined until the end points are specified
Formulae:
∫ xn dx = xn+1⁄(n+1)+ c
∫ k .dx = kx + c
Trigonometry rules:
Example 1: ∫ x4 .dx
4x2 + c (b) 4x3 + c (c) x3⁄3 + c (d) x5⁄5 + c
Answer: d
Explanation: Here n = 4
∫ x4 dx = x(4+1)⁄(4+1) + c
= x5⁄5 + c
Example 2: ∫(8ex- 2⁄x2 + 3x2 -2x). dx
Answer:
8 ∫ex . dx - 2 ∫x-2 . dx + 3 ∫x2 .dx - 2 ∫x .dx
= 8ex – 2.x-1⁄-1 + 3. x3⁄3 - 2. x2⁄2 + c
= 8ex + 2⁄x + x3 - x2 + c
