Chapter 5.2, Problem 34E

Approximating definite integrals Complete the following steps for the given integral and the given value of n.

1. a. Sketch the graph of the integrand on the interval of integration.
2. b. Calculate ∆x and the grid points x₀, x₁, … , x_n, assuming a regular partition.
3. c. Calculate the left and right Riemann sums for the given value of n.
4. d. Determine which Riemann sum (left or right) underestimates the value of the definite integral and which overestimates the value of the definite integral.

56. ${\displaystyle {\int }_0^{\pi /2}\cos xdx}$; n = 4