Left and right Riemann sums Complete the following steps for the given function, interval, and value of n.
{Use of Tech} ƒ(𝓍) = cos 𝓍 on [0. π/2]; n = 4
(d) Calculate the left and right Riemann sums.

Approximating displacement The velocity of an object is given by the following functions on a specified interval. Approximate the displacement of the object on this interval by subdividing the interval into n subintervals. Use the left endpoint of each subinterval to compute the height of the rectangles.

v = [1 / (2t + 1)] (m/s), for 0 ≤ t ≤ 8 ; n = 4

Approximating displacement The velocity of an object is given by the following functions on a specified interval. Approximate the displacement of the object on this interval by subdividing the interval into n subintervals. Use the left endpoint of each subinterval to compute the height of the rectangles.

{Use of Tech} v = 4 √(t +1) (mi/hr) . for 0 ≤ t ≤ 15 ; n = 5     

Left and right Riemann sums Use the figures to calculate the left and right Riemann sums for f on the given interval and for the given value of n.

ƒ(𝓍) = x + 1 on [1,6] ; n = 5

Left and right Riemann sums Complete the following steps for the given function, interval, and value of n.

f(x) = x + 1 on [0,4]; n = 4

(d) Calculate the left and right Riemann sums.                                                                                                                                                

Left and right Riemann sums Complete the following steps for the given function, interval, and value of n.

ƒ(𝓍) = x² ─ 1 on [2,4]; n = 4

(d) Calculate the left and right Riemann sums. 

Left and right Riemann sums Complete the following steps for the given function, interval, and value of n.

{Use of Tech} ƒ(𝓍) = e ˣ/₂ on [1,4]; n = 6

(d) Calculate the left and right Riemann sums. 

A midpoint Riemann sum Approximate the area of the region bounded by the graph of ƒ(𝓍) = 100 ― x² and the x-axis on [0, 10] with n = 5 subintervals. Use the midpoint of each subinterval to determine the height of each rectangle (see figure).

Free fall On October 14, 2012, Felix Baumgartner stepped off a balloon capsule at an altitude of almost 39 km above Earth’s surface and began his free fall. His velocity in m/s during the fall is given in the figure. It is claimed that Felix reached the speed of sound 34 seconds into his fall and that he continued to fall at supersonic speed for 30 seconds. (Source: http://www.redbullstratos.com)

(a) Divide the interval [34, 64] into n = 5 subintervals with the gridpoints x₀ = 34 , x₁ = 40 , x₂ = 46 , x₃ = 52 , x₄ = 58 , and x₅ = 64. Use left and right Riemann sums to estimate how far Felix fell while traveling at supersonic speed.