Indefinite Integral

Indefinite Integral 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 its value cant 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) x33 + c (d) x55 + c Answer: d Explanation: Here n = 4 x4 dx = x(4+1)(4+1) + c = x55 + c Example 2: (8ex- 2x2 + 3x2 -2x). dx Answer: 8 ex . dx - 2 x-2 . dx + 3 x2 .dx - 2 x .dx = 8ex 2.x-1-1 + 3. x33 - 2. x22 + c = 8ex + 2x + x3 - x2 + c