# Windshield Wiper function

1. Feb 10, 2005

### 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, unfortunetly i missed the class in which he told us this. But from the notes, there isn't much explaination. 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.

2. Feb 10, 2005

### MathStudent

is this the function?

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

3. Feb 10, 2005

### Integral

Staff Emeritus
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.

4. Feb 10, 2005

### matrix_204

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