value of definite integral of greatest integer function

[karan]

What is definite integral of [x],where [x] denotes the greatest integer less than or equal to x, from limit 0 to3

 

[royhaas]

Re: definite integral

You are integrating a step function.

 

[Deleted member 4993]

Re: definite integral

What is definite integral of [x],where [x] denotes the greatest integer less than or equal to x, from limit 0 to3

Draw an approximate sketch of the function within the given domain.

That will give you an idea about what the "antiderivative should look like - then "add" up.

 

[galactus]

As SK said, add up the area of the rectangles. This is actually a fairly easy integral, though some may be put off at first.

If you have \(\displaystyle \int_{0}^{n}{[x]}dx\)

Then the area will be \(\displaystyle \frac{n(n-1)}{2}\)