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.

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- December 7th 2006, 08:27 AMmyoplex11integration 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. - December 7th 2006, 08:32 AMAfterShock
- December 7th 2006, 08:42 AMmyoplex11
this is the problem we had on our practice exam

- December 7th 2006, 08:51 AMThePerfectHacker
- December 7th 2006, 08:52 AMThePerfectHacker
- December 7th 2006, 08:52 AMPlato
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