Basic mathematics | chapter 0 | class 11 NCERT

#integration
Integration rules are mathematical rules that allow us to find the antiderivative or integral of a function. Integration is the reverse process of differentiation and is used in calculus to find areas, volumes, and solve various problems involving accumulation.

Some common integration rules include:

1. Power Rule: This rule states that if we have a function of the form f(x) = x^n, where n is a constant (except -1), then the integral is given by ∫f(x) dx = (1/(n+1))x^(n+1) + C, where C is the constant of integration. For example, ∫x^3 dx = (1/4)x^4 + C.

2. Constant Rule: This rule states that if we have a constant function, f(x) = c, where c is a constant, then the integral is given by ∫f(x) dx = cx + C. For example, ∫5 dx = 5x + C.

3. Sum Rule: This rule states that if we have a sum of two functions, f(x) + g(x), then the integral of the sum is equal to the sum of the integrals of each function. ∫(f(x) + g(x)) dx = ∫f(x) dx + ∫g(x) dx.

4. Substitution Rule: This rule allows us to simplify integrals by substituting a new variable or expression. If we have an integral of the form ∫f(g(x))g'(x) dx, then we can substitute u = g(x) and rewrite the integral in terms of u. This can help us simplify the integral and solve it using known integration rules.

These are just a few examples of integration rules, and there are many more that can be used depending on the specific function and situation. These rules provide a systematic approach to finding antiderivatives and are essential tools in calculus and mathematical analysis.