Calculus Projects

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Calculus Projects deal with two most important parameters of Mathematics and Physics. It deals with the

solution of the problems where we need to find the derivative and integration of the function. Here the

function can be algebraic, trigonometric, exponential, or any other function. So calculus project helps in the

step by step evaluation of the problems, which involves differentiation and integration.


This can be better clarified by taking individual examples of differentiation and integration. The examples are

as shown below:- 



Example 1:- Find the derivative of the Sin (2x)


Solution 1:- Given function is Sin (2x)

To find: - d/dx Sin (2x)

 We know that,d/dx (Sinx) = Cos x

 Therefore, d/dx Sin (2x) = Cos (2x). d/dx (2x) (because it is a composite function).

 So d/dx Sin (2x) = Cos (2x). 2

 Therefore, d/dx Sin (2x) = 2. Cos (2x)

Hence d/dx Sin (2x) = 2. Cos (2x). This is the project problem of calculus. Here we have solved

one part of calculus that is known as differentiation.


Example 2:- Find the integration of ∫ x3 dx


Solution 2:- Given function is x3.

 Here we have to find the integration of x3.

 Now we know that,∫xn.dx  = xn+1/ n+1 + c, Here c is constant of integration

Therefore,∫ x3 dx = ( x3+1/ 3+1) + c = x4/4+ c

So the integration of ∫ x3 dx = x4/4+ c

In this example c is constant of integration. And in this example we have evaluated the important

part of calculus that is known as integration.

 

 
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