A≈Ln=f(x0)Δx+f(x1)Δx+⋯+f(xn−1)Δx=∑i=1nf(xi−1)Δx
∫abf(x)dx
limn→∞∑i=1nf(a+n(i−1)(b−a))⋅n(b−a)
height: f(a+n(i−1)(b−a))
width: n(b−a)
Rn is Ln but ending at i instead of i−1
∫ab[f(x)+g(x)]=∫abf(x)+∫abg(x)
∫abcf(x)=c∫abf(x)
∫abf(x)=∫acf(x)+∫cbf(x)
average value: favg=b−a1∫abf(x)