Question 10Let f(x)=2x³ over the interval [1,2] .Find a formula for the Riemann sum obtained by dividing the interval [1 , 2] into n equal sub-intervals and using the right endpoint for each ck .Then, take a limit of these sums as n→∞ to calculate the true area under the graph of f over [1,2].Show and explain ALL your work

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Answered: Question 10 Let f(x)=2x over the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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find the n=100 Riemann Sum approximations for the area under f(x) = 2x+1 on you could use this desmos Riemann Sum calculator [1,4]. Using the "Relative" option, • calculate the Riemann Sum using each subinterval's "right endpoint" (Right Sum) • calculate the Riemann Sum using each subinterval's "left endpoint" (Left Sum) ✩Finally, subtract to find the difference between the two estimates. Your answer should be positive, and it should have two digits after the decimal point.
Consider the function f(x)=x3 on the interval [8,20]. Let P be a uniform partition of [8,20] with 600 sub-intervals. Compute the right Riemann sum of f on the partition. If needed, round your answer to three decimals. do not use calculator
2. Use the Riemann sums to calculate the exact area under the curve and above the axis a) f(x) = 2x³ - 3x² +1, in the interval [0,2]. b) f(x) = x² + 3, in the interval [1,3]. c) f(x) = x¹-x² + 1 in the interval [2, 5].
(a) Express the area under the curve y =x4 +5x2 +xfrom 2 to 7 as a limit.(b) Use a computer algebra system to evaluate the sum inpart (a).(c) Use a computer algebra system to find the exact areaby evaluating the limit of the expression in part (b).
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Use the Riemann Sum to find the area of the region bounded by the graph of f(x)=tan(x/6) and the x-axis between x = 0 and x = 2π. Write out the expression of the summation, but don’t evaluate it.
The question is attached
The density of cars (in cars per km) down a 30-km stretch of Hume highway is approximated by the function g(x) = 150(1+ sin 4x) a) Write a Riemann sum that approximates the total number of cars on this 30-km stretch b) Find the total number of cars on that stretch
Express the limit as a definite integral on the given interval. n x* lim (xF)2 + 2 Ax, [1, 7] (x*)2 + 2 i = 1 dx
We want to use a left Riemann sum to estimate the value of the definite integral. a) If we divide the interval [5,7] into 4 sub-intervals of the same length, we obtain 4 intervals of the form [xi,xi+1] whose union gives the interval [5,7]. Give the ends of these intervals starting from the left and going to the right. Don't forget the square brackets and list your answers separated by commas. Answer: [x0,x1,…,x4]= b) Calculate the value ti of each of the terms of the Riemann sum on the left and list your answers starting from the left and going to the right. Give exact values. Don't forget the square brackets and list your answers separated by commas.Answer: [t0,t1,…,t3]= c) Calculate the value of the left Riemann sum. Give your answer with a precision of at least two decimal places.Answer:
Determine the Riemann sum using L4 over the interval [-1,1]. y = 3x² - 2x + 1

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Question 10 Let f(x)=2x over the interval [1,2] . Find a formula for the Riemann sum obtained by dividing the interval [1 ,2] into n equal sub-intervals and using the right endpoint for each c. Then, take a limit of these sums as n→0 to calculate the true area under the graph of f over [1,2].