integral sinx 4

? If the derivative of a function is given, then the function itself is called anti-derivative or integral. We illustrate it with the help of an example. Consider the function f(x) = x 4 then its derivative is given by f ' (x) = 4x 3 . The question arises: given f ' (x..

Definite Integrals Animation..

Animation Indefinite Integrals..

..

..

Let f(x) = 3x 2 Note that for different values of C we get different integrals. But all these integrals are very similar geometrically. The function y = x 3 + C represent a family of integrals. The above figure shows different curves of the integral function ..

When the integrand consists of trigonometric function, we use suitable trigonometric identities to simplify the function so that it can be integrated. Few identities are given below for ready reference. (1) (2) (3) (4) (5) (7) (..

Indefinite Integrals as Antiderivative - Consider the following example: Let f(x) = cos 3x, let us find a function F(x) such that We know that Here In other words we say the integral cos 3x is Suppose then also we ha..

(1) Let be rational function. If is improper, divide P(x) by Q(x). Let T(x) be the quotient and P 1 (x) be the remainder, then Where T(x) is a polynomial and is a proper rational function. (2) Resolve the proper rational function in to partial fractions. (3) Write as sum of partial fractions. (..

], which is shown in the figure. Being a rectangular region, the area of f(x) = 2 bounded by X- axis, x = 1 and x = 2 is given by base X height, the height being equal to Base = (2 - 1) = 1 units, height = 2 units This region is triangular above the axis bounded by x = 0 and x = 1. The area of this..