Question

Are these all the same? #1. A=lim as n approaches infinity of sigma ("n" on top of sigma, i=1 on bottom of sigma) f(x subscript i)times delta x #2. A=same as the above until sigma, times f(x subscript i-1) times delta x #3. A=same as above till' sigma, f(xi*) times delta x....this is for integrals, areas under curves

Answer 1

No i believe #1 gives upper bounds area and #2 gives lower bounded area, not sure about #3 can you rewrite that part

Answer 2

A=lim as n approaches infinity, sigma (on top of sigma it says "n", bottom of sigma it says "i=1") and then f[xi (note, theres a * star symbol on top of i)]delta x

Answer 3

\[A=\lim_{n \rightarrow \infty}\sum_{i=1}^{n} f(x*i)Deltax\] Note: where it says f(x*i), I meant the * is right on top of the i, which is a subscript of x)

Answer 4

All I know is that * has something to do with sample points, but I dont get that part

Answer 5

ok i think it has to do with taking the midpoint between xi and xi-1, ->f(xi-1 + deltax/2) this will give an area between the upper and lower bounds yielding a more accurate approximation of the actual area under the curve

Answer 6

Thank you!