integration and the greatest function help exam in 7 hrs
integrate f(x) from 0 to n. where n is a positive integer and f(x) is the greatest integer function.
I Know that i have to use the definiton of greatest integer function and break it into sum of the integrals how do i do this.
integrate f(x) from 0 to n. where n is a positive integer and f(x) is the greatest integer function.
I Know that i have to use the definiton of greatest integer function and break it into sum of the integrals how do i do this.
F(b) - F(a) is the signed area, where a and b are the limits of integration (from a to b).
In this case, your b is n and 0 is a. Do you have a specific problem?
integrate f(x) from 0 to n. where n is a positive integer and f(x) is the greatest integer function.
I Know that i have to use the definiton of greatest integer function and break it into sum of the integrals how do i do this.
Okay.
A defined function on a closed interval is Riemann integrable if and only if it is continous almost everywhere.
We we need to find,
Since it is continous almost everywhere we can use the subdivision rule,
If you draw a graph for say n=8, you will see a series of seven ‘stair steps’.
The area under the ‘stairs’ is the sum of the areas of seven rectangles.
So 1+2+3…+7. To do it for n we get a sum of