Question

Estimate the value of the definite integral
∫ 7
1 (3/x)dx
by computing left-hand and right-hand sums with 3 and 6 subdivisions of equal length.

A. n=3 left-hand sum =

B. n=3 right-hand sum =

C. n=6 left-hand sum =

D. n=6 right-hand sum =

Answer 1

I'll do one; you can try the others. Post your work if you get stuck. There are online Riemann Sum calculators you can use.

f(x) = 3/x
with 6 subintervals, that gives you
∆x = (7-1)/6 = 1
Right Sum = 1*(f(2)+f(3)+f(4)+f(5)+f(6)+f(7))
= 3/2 + 3/3 + 3/4 + 3/5 + 3/6 + 3/7 = 669/140

Answer 2

thanks man!