How do you find the integral of the greatest integer function?

Originally Answered: How do I integrate the greatest integer function? Greatest integer function is discontinuous at all integers. So you should write the definition of the function in each of the smaller intervals in which it’s value will be different and then integrate. Sum of integrals equals integral of sum.

Why can’t e x 2 be integrated?

This is because, you cannot integrate this function directly, no direct formula and even if you make substitution, a function will come in the denominator, which will never get eliminated. Like you may get an algebric or logarthimic function, which on integrating through by parts will not terminate.

What is the greatest integer function?

Greatest Integer Function is a function that gives the greatest integer less than or equal to the number. The greatest integer less than or equal to a number x is represented as ⌊x⌋. We will round off the given number to the nearest integer that is less than or equal to the number itself.

What is the derivative of greatest integer function?

So I know that the derivative of the greatest integer function is zero. That is if f(x)=[x] then df/dx=0.

How do you find the integral of an ex?

What is the Integral of e^x? The integral of ex is ex + C. Symbolically it is written as ∫ ex dx = ex + C, where C is the integration constant.

Does ∫ Ex 2 DX exist?

There is no nice, finitely expressible antiderivative. (Other that to write: ∫ex2dx , of course.) +⋯=1+x+x22+x36+⋯ (for all x ), it follows that ex2=1+x2+x42+x66+⋯ (for all x ).

What is greatest integral value?

The greatest Integer Function [X] indicates an integral part of the real number which is the nearest and smaller integer to. . It is also known as the floor of X. [x]=the largest integer that is less than or equal to x.

How do you integrate ex?

Since the integral is the inverse operation of differentiation, the integral of ex is also ex. i.e., ∫ ex dx = ex + C. Here, C is the integration constant.