Estimate the area

Question

f(x)=1/x+8 from x=0 to x=5 using a Riemann sum with n=10 subintervals with both left and right endpoints

Answer 1

Let do right Riemann sum: Δx = (5 - 0)/10 = 0.5; R₁₀ = ∑₁¹⁰1/(0.5i + 8)·0.5 = 0.4737.

Then we evaluate left rieman sum: L₁₀ = ∑₀⁹[1/(0.5i + 8)·0.5 = 0.4977

We consider f(x) = 1/(x + 8) because if function f(x) = 1/x + 8 left Riemann sum DNE for interval [0, 5].

For calculation I used TI-84 sum(seq) command from List menu

Answer 2

Riemann Sum (lower): Sum from i =1 to 10 of ((1/x_i-1) +8)(5/10) with x_j = 0 + (5/10)j

The higher sum is the same except you sub in 1/x_i for 1/x_i-1

5 range/ 10 intervals is the Δx.

Make a table with x values and f(x) values. That makes it easier.

Good luck!