Calculus Practice is very essential as it involves lot of methods and formulas. This involves basic two
important parts. One is known as differential calculus and other is known as Integral calculus. Both
differential and integral calculus has so many formulas and methods, that without practice one cannot
understand or have sound control over it. So Calculus practice tool is helped in getting thorough knowledge
of the subject.
Two of the practice examples are shown below.
Example 1:- Find the derivative of the x. ex.
Solution 1:- Given function is x. ex.
To find: - d/dx (x. ex)
We know that,
d/dx (ex) = ex
Therefore, d/dx (x. ex ) = x. d/dx ex + ex d/dx (x)
So, d/dx (x. ex) = x. d/dx ex + ex d/dx (x)
Therefore, d/dx (x. ex) = x. ex + ex. (1) = x. ex + ex.
Hence d/dx (x. ex) = x. ex + ex. This is the practice problem of differential calculus.
Example 2:- Find the integration of ∫ x10 dx
Solution 2:- Given function is x10.
Here we have to find the integration of x10.
Now we know that,
∫xn. dx = xn+1/ n+1 + c, Here c is constant of integration
Therefore,∫ x10 dx = ( x10+1/ 10+1) + c = x11/11+ c
So the integration of ∫ x10 dx = x11/11+ c