Question

help please...Riemann sum: f(x) = 1/x on interval [1,6]; and n=5...

Answer 1

\[\sum_{i=1}^{n} f(x i*) dx\]

Answer 2

ok n = 5 right?

Answer 3

so we divide the interval [1,6] into 5 parts
we can use left hand endpoints or right hand endpiont so make life easy
if we use left hand enpoints they are 1, 2, 3, 4, 5

Answer 4

WHY CANT WE USE TRAP!

Answer 5

so
\[\sum_{k=1}^5 f(x_k)\Delta x =1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5} \]

Answer 6

here since you are dividing the interval of length 5 into 5 parts, \(\Delta x=1\)

Answer 7

thank you

Answer 8

how about for 2x+1 (1,4) n=6

Answer 9

would it be 3 parts.. and dx = 1/2 ...i first plugged in f(1) = 2(1) +1 x 1/2...... but in order to get the right answer i must start at 1.5... i dont understand why