solve all parts please Complete the following steps for the given function inter

Question

solve all parts please

Complete the following steps for the given function interval and value of n. Sketch the graph of the function on the given interval. Calculate Delta x and the grid points x0, x1, , xn. Illustrate the left and right Riemann sums, and determine which Riemann sum underestimates and which sum overestimates the area under the curve. Calculate the left and right Riemann sums. f(x) = 2x2 + 3 for [3,8]; n=5 Sketch the graph of f(x) = 2x2 + 3 on the interval [3, 8]. Choose the correct graph below.

Explanation / Answer

b ) delta x = 1 x0 = 3 and x1 = 4 and x2 = 5 and x3 = 6 and x4 = 7 and x5 = 8

c and d) Right reiman sum = 1 * { 35 + 53 + 75 + 101 + 131 } = 395

Left reiman sum = 1 * { 21 + 35 + 53 + 75 + 101 } = 285

Left reiman sum underestimates and right reiman sum over estimates

Gor graph d) is the answers because f (8) = 131 and concave upwars as f ' '(x) > 0

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