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