For the function given below, find a formula for the Riemann sum obtained by dividing the interval [a,b] into n equal subintervals and using the right-hand endpoint for each c. Then take a limit of this sum as n → ∞ to calculate the area under the curve over [a,b]. f(x) = 5x + 11x over the interval [0,1]. Find a formula for the Riemann sum.

Definition: A function ƒ : R → R is said to be periodic with period L if f(x + L) = f(x) for every x E R. Consider the space P of continuous periodic functions on R with period 27 such that π [** f(x) dx = 0 A

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Complete the following steps for the given function f and interval. a. For the given value of n, use sigma notation to write the left, right, and midpoint Riemann sums. Then evaluate each sum using a calculator. b. Based on the approximations found in part (a), estimate the area of the region bounded by the graph of f on the interval. f(x) = cos 2x for 0, n= 40 a. Write the left Riemann sum. 40 Σ k= 1 (Type an exact answer, using n as needed.)