Consider f(x)=ln(1+x) on the interval [0,2].
(a) Divide [0,2] into n equal subintervals and derive an explicit formula for the approximation Rn of ∫02f(x)dx that uses the right endpoints of the subintervals.
(b) Evaluate n→∞limRn and demonstrate that this limit equals the exact value of the definite integral.
(c) Determine the least integer n such that ∣Rn−∫02f(x)dx∣<0.01. Justify your answer.
a. (a)
b. (b)
c. (c)