in this problem you will calculate the area between fxx2 and the x axis over the interval 311 us

To begin, we divide [3,11] into ? equal width subintervals [?0,?1],[?1,?2],…,[???1,??] each of w

Question

In this problem, you will calculate the area between ð‘“(ð‘¥) = ð‘¥^2 and the ð‘¥-axis over the interval [3,11] using a limit of right-endpoint Riemann sums: Area = limð‘›â†’âˆž (âˆ‘ð‘˜=1ð‘› ð‘“(ð‘¥ð‘˜)Î”ð‘¥). Express the following quantities in terms of ð‘›, the number of rectangles in the Riemann sum, and ð‘˜, the index for the rectangles in the Riemann sum. We start by subdividing [3,11] into ð‘› equal width subintervals [ð‘¥0,ð‘¥1], [ð‘¥1,ð‘¥2], ..., [ð‘¥ð‘›âˆ’1,ð‘¥ð‘›] each of width Î”ð‘¥. Express the width of each subinterval Î”ð‘¥ in terms of the number of subintervals ð‘›. Î”ð‘¥ = Find the right endpoints ð‘¥1, ð‘¥2, ð‘¥3 of the first, second, and third subintervals [ð‘¥0,ð‘¥1], [ð‘¥1,ð‘¥2], [ð‘¥2,ð‘¥3] and express your answers in terms of ð‘›. ð‘¥1, ð‘¥2, ð‘¥3 = (Enter a comma-separated list.) Find a general expression for the right endpoint ð‘¥ð‘˜ of the ð‘˜th subinterval [ð‘¥ð‘˜âˆ’1,ð‘¥ð‘˜], where 1 â‰¤ ð‘˜ â‰¤ ð‘›. Express your answer in terms of ð‘˜ and ð‘›. ð‘¥ð‘˜ = Find ð‘“(ð‘¥ð‘˜) in terms of ð‘˜ and ð‘›. ð‘“(ð‘¥ð‘˜) = Find ð‘“(ð‘¥ð‘˜)Î”ð‘¥ in terms of ð‘˜ and ð‘›. ð‘“(ð‘¥ð‘˜)Î”ð‘¥ = Find the value of the right-endpoint Riemann sum in terms of ð‘›. âˆ‘ð‘˜=1ð‘› ð‘“(ð‘¥ð‘˜)Î”ð‘¥ = Find the limit of the right-endpoint Riemann sum. limð‘›â†’âˆž (âˆ‘ð‘˜=1ð‘› ð‘“(ð‘¥ð‘˜)Î”ð‘¥) =

          In this problem, you will calculate the area between ð‘“(ð‘¥) = ð‘¥^2 and the ð‘¥-axis over the interval [3,11] using a limit of right-endpoint Riemann sums:
Area = limð‘›â†’âˆž (âˆ‘ð‘˜=1ð‘› ð‘“(ð‘¥ð‘˜)Î”ð‘¥).
Express the following quantities in terms of ð‘›, the number of rectangles in the Riemann sum, and ð‘˜, the index for the rectangles in the Riemann sum.
We start by subdividing [3,11] into ð‘› equal width subintervals [ð‘¥0,ð‘¥1], [ð‘¥1,ð‘¥2], ..., [ð‘¥ð‘›âˆ’1,ð‘¥ð‘›] each of width Î”ð‘¥. Express the width of each subinterval Î”ð‘¥ in terms of the number of subintervals ð‘›.
Î”ð‘¥ = 
Find the right endpoints ð‘¥1, ð‘¥2, ð‘¥3 of the first, second, and third subintervals [ð‘¥0,ð‘¥1], [ð‘¥1,ð‘¥2], [ð‘¥2,ð‘¥3] and express your answers in terms of ð‘›.
ð‘¥1, ð‘¥2, ð‘¥3 = 
(Enter a comma-separated list.)
Find a general expression for the right endpoint ð‘¥ð‘˜ of the ð‘˜th subinterval [ð‘¥ð‘˜âˆ’1,ð‘¥ð‘˜], where 1 â‰¤ ð‘˜ â‰¤ ð‘›. Express your answer in terms of ð‘˜ and ð‘›.
ð‘¥ð‘˜ = 
Find ð‘“(ð‘¥ð‘˜) in terms of ð‘˜ and ð‘›.
ð‘“(ð‘¥ð‘˜) = 
Find ð‘“(ð‘¥ð‘˜)Î”ð‘¥ in terms of ð‘˜ and ð‘›.
ð‘“(ð‘¥ð‘˜)Î”ð‘¥ = 
Find the value of the right-endpoint Riemann sum in terms of ð‘›.
âˆ‘ð‘˜=1ð‘› ð‘“(ð‘¥ð‘˜)Î”ð‘¥ = 
Find the limit of the right-endpoint Riemann sum.
limð‘›â†’âˆž (âˆ‘ð‘˜=1ð‘› ð‘“(ð‘¥ð‘˜)Î”ð‘¥) =

Added by Lori W.

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