Estimate the area under the graph.

Question

Estimate the area under the graph of f(x) = 1/(x+4) over the interval [-2.3} using five approximating rectangles and Right endpoints. 

Rn= ----

Repeat the approximation using left endpoints.

Ln= ---

Answer 1

f(x) = 1/(x+4)   Δx = (3-(-2)) / 5 = 1

 

R₅ = f(-1)Δx + f(0)Δx + f(1)Δx + f(2)Δx + f(3)Δx

 

     = 1/3 + 1/4+ 1/5+ 1/6 + 1/7

 

L₅ = f(-2)Δx + f(-1)Δx + f(0)Δx + f(1)Δx + f(2)Δx

 

     = 1/2 + 1/3 + 1/4 + 1/5 + 1/6

 

Answer 2

0.2(1/6.2 + 1/6.4 + 1/6.6 + 1/6.8 + 1/7) = your answer for R_n.

 

I bet you can figure the other.