1. Mathematics
2. Calculus and Analysis
3. Real Analysis
4. Integrals
5. 279529

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Are these functions Reimann Integrable? I am just learning this topic, so my description may not be accurate. A function is Reimann Integrable if it's Upper Darboux Sums and Lower Darboux suns are equal.

Or stated another way, if U(f, P) - L(f, P) < e

The two functions are piecewise functions.

1) f(x) = { 0 when x = 0
1/n when x is in (1/(n+1) , 1/n]
}

Show that F(x) is Reimann Integrable on [0,1]

2) f(x) = { sin(PI/x) if 0 < x <= 1
0 if x = 0
}

Also show that F(x) is Reimann Integrable