What is the significance of the Windshield Wiper function in calculus?

[matrix_204]

It says that; Let f be continuous on [a,b]. Define a new function F on [a,b] as follows; For all x in [a,b], F(x)=int(a-x)f=int(a-x)f(t)dt.

My teacher likes to call this the windshield wiper function, unfortunately i missed the class in which he told us this. But from the notes, there isn't much explanation. So i was wondering if anyone knows what this function actually says, since i was trying to find in my book too but its hard without knowning the name used in texts, if there is such a thing.

 

[MathStudent]

is this the function?

$$F(x) = \int_{a}^{x} f = \int_{a}^{x} f(t) dt$$

 

[Integral]

Your notation is not clear. I am not sure I understand you.

Is this what your are shooting for.

$$F(x) = \int (a-x) f(x) dt$$

click on the above equation to see how it was created. Review this thread to learn to use our LaTex equation language. This will enable you to clearly present your equations.

 

[matrix_204]

yes sorry bout that, math student has it right, that's the one, btw i figured it out a bit like my classmate was tellin me not to worry and just now the antiderivative definition. so its not as important, but i have another question instead, what type of function is bounded on a closed interval but is nonintegrable