Algebraic Integration Notes
●Algebraic integration is the process of finding the antiderivative of a function,
which is also known as the indefinite integral.
●The indefinite integral of a function can be represented as:
∫f(x) dx = F(x) + C
where F(x) is the antiderivative of f(x), and C is the constant of integration.
●The constant of integration represents the fact that there are an infinite number
of functions that can be derived from a given function.
●To find the indefinite integral of a function, you can use the following rules:
1. Constant rule: If f(x) = C (a constant), then ∫f(x) dx = Cx + C
2. Power rule: If f(x) = x^n (n is a constant), then ∫f(x) dx = (x^(n+1))/(n+1) + C
3. Constant multiple rule: If f(x) = Cg(x) (C is a constant), then ∫f(x) dx = C∫g(x) dx
4. Sum rule: If f(x) = g(x) + h(x), then ∫f(x) dx = ∫g(x) dx + ∫h(x) dx
5. Difference rule: If f(x) = g(x) - h(x), then ∫f(x) dx = ∫g(x) dx - ∫h(x) dx
●To find the definite integral of a function, you can use the following formula:
∫baf(x) dx = F(b) - F(a)
where a and b are the lower and upper limits of the integral, and F(x) is the antiderivative
of f(x).
