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**Differentiation and integration**can help us solve many types of real-world problems. ...**Integration**, in**mathematics**, technique of finding a function g(x) the derivative of which, Dg(x), is equal to a given function f(x). This is indicated by the integral sign “∫,” as in ∫f(x), usually called the indefinite integral of the function. ...- Remember also that, while your A Level course may offer a somewhat rigid approach to learning techniques related to Differentiation and Integration, you will
**have the opportunity in future to learn different patterns, some that may even be self-taught,**if**you ever decide to follows steps and processes without the aid of a computer.**Or you can learn them with maths **Differentiation****and****Integration**Rules A derivative computes the instantaneous rate of change of a function at different values. An indefinite integral computes the family of functions that are the antiderivative. A definite integral is used to compute the area under the curve- 1) If y = x n, dy/dx = nx n-1 2) If y = kx n, dy/dx = nkx n-1 (where k is a constant- in other words a number) Therefore to differentiate x to the power of something you bring the power down to in front of the x, and then reduce the power by one. Examples If y = x 4, dy/dx = 4x 3 If y = 2x 4, dy/dx = 8x 3 If y = x 5 + 2x -3, dy/dx = 5x 4 - 6x -4
- Handwritten Notes by Dr. Siddharth Raj (Mbbs)