Calculus Problem

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Calculus Problem involves two important types of problems. One is known as integral calculus and other one

is known as differential calculus. Both of these involve certain rules and regulations, which needs to be

understood before doing its actual calculation. Calculus Problem is generally involved various functions

including complex variables also. Apart from this, this also helps in determing or solving the various Physics

equations. This is very useful tool to generate a solution from very small information available. This is

because if we have only one strip related information we can generate complete figure information by

integrating with the limits specified.

This can be easily understood by taking the separate examples of the integral calculus and differential

calculus.



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


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

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

 We know that,d/dx (Cosx) = -Sin x

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

 So d/dx Cos (2x) = -Sin 2x. (2 )

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

Hence d/dx Cos (2x) = -2.Sin 2x.

This is one of the calculus problem . Here we have solved one part of calculus that is known as

differentiation.



Example 2:- Find the integration of ∫ x2 dx


Solution 2:- Given function is x2.

Here we have to find the integration of x2.

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

Therefore,

  ∫ x2 dx = (x2+1/ 2+1) + c

  x2/3+ c

So the integration of ∫ x2 dx = x3/3+ c, Here , c is constant of integration.


 

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