Question

Estimate the area under the graph of f(x)=1/x^2 +1 over the interval [2,7] using five approximating rectangles and right endpoints.

Rn= ?

Repeat the approximation using left endpoints.

Ln= ?

Report answers accurate to 4 places.

Answer 1

Assuming you meant f(x) = 1/(x^2+1) we have
Left = f(2) + f(3) + f(4) + f(5) + f(6) = 1/5 + 1/10 + 1/17 + 1/26 + 1/37 = 0.4243
Right = f(3) + f(4) + f(5) + f(6) + f(7) = 1/10 + 1/17 + 1/26 + 1/37 + 1/50 = 0.2443

Answer 2

Rn = 11.7705
Ln = 11.7706