Calculus Practice Problems are the very effective means to have sound knowledge about the method of
solving calculus problems. Generally calculus problem involves two important parts. One is of differential
calculus and other is of integral calculus. If we will practice calculus problems then only we will have sound
knowledge of the subject and hence we can able to solve complicated problems very easily.
This can be understood by the given below examples:-
Example 1:- Find the derivative of the x logx
Solution 1:- Given function is x logx
To find: - d/dx (x logx)
We know that,
d/dx (x logx) = x d/dx (log x) + logx d/dx(x)
Therefore, d/dx (x logx) = logx. d/dx (x) + x d/dx (logx)
So d/dx (x logx) = log x + x. 1/x
Therefore, d/dx Sin (2x) = log x + 1
Hence d/dx Sin (2x) = log x + 1.
Example 2:- Find the integration of ∫ x + 2 dx
Solution 2:- Given function is x + 2
Here we have to find the integration of x + 2
Now we know that,
∫xn.dx = xn+1/ n+1 + c, Here c is constant of integration
Therefore,∫ x + 2 dx = (x1+1/ 1+1) + 2 x + c = x2/2+2x+c
So the integration of ∫ x + 2 dx = x2/2+2x+c
In this example c is constant of integration. This is the example of integral calculus.