A car is entering the highway, and accelerates in the first 30 seconds, as follows: time (in seconds) 0 6 12 18 24 30 speed (in meters per second) 2 10 16 20 23 25 Use a Riemann sum, with 5 equal subintervals, to overestimate the distance travelled by the car over these 30 seconds. Would you use left- or right-endpoints in your estimation? Explain.

Q: Approximate the region under the curve f(x) = x^2 by using the Riemann sum with 3 intervals using…

A: Given, upper limit= b=14 lower limit = a= 2 number of intervals= n=3 We first have to find the width…

Q: Write the Formula for the Riemann Sum with Equal-Width Subintervals?

A: Write the Formula for the Riemann Sum with Equal-Width Subintervals?

Q: Evaluate the Riemann sum for f(x) = x^2 − x where 0 ≤ x ≤ 2 with four subintervals, taking the…

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Q: A car is entering the highway, and accelerates in the first 30 seconds, as follows: time (in…

A: Given that Time(in seconds) 0 6 12 18 24 30 Speed(in m/s) 2 10 16 20 23 25 To find the total…

Q: Approximate the region under the curve f(x) = 2x + 1 by using the Riemann sum with 3 intervals using…

A: Width of each interval= (21-3)/3=18/3=6 so the partition is 3,9,15,21 For left Riemann sum we take…

Q: Use the given graph to estimate the left Riemann sum for the given interval with the stated number…

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Q: Write Va dx as the limit of Riemann sums with equal length subintervals using RIGHT ENDPOINTS as…

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Q: Evaluate the Riemann sum for f(x) = 3- 1/2 x , 2<=x <= 14 ,with six subintervals, taking the…

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Q: The velocity of an object v, in meters per second, is measured every 15 seconds. | (seconds) 0 15 30…

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Q: If f(x) = 2x2 - 7,0 sxs 3, find the Riemann sum with n = 6, taking the sample points to be…

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Q: 1. Use the definition of the definite integral as the limit of a Riemann sum to evaluate

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Q: Approximate the area between the graph of f(x)=x^3 and the x-axis on the interval [3,5] by using a…

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Q: Estimate f, f(x)dæ from the graph using a (a) Left-hand Riemann sum with 4 subintervals of equal…

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Q: Estimate the area under the curve y=(x^2)+1 between x=0 and x=1 using Reimann Sums with four…

A: Given, y=x2+1 a,b=0,1 n=4 ∆x=b-an=1-04=14 The four intervals are, 0,14,14,24,2434,34,1 The right…

Q: find the riemann sum

A: Given  fx=2x2-8 , 0≤x≤3 and  n=6

Q: 5) Approximate x²-1|dx with a right-endpoint Riemann sum using four equal subintervals.

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 3. Use the Riemann sum as no to evaluate (r- 2)'dr

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Use the given graph to estimate the left Riemann sum for the given interval with the stated number…

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Q: If f(x) = 8x2 − 5x, 0 ≤ x ≤ 3, evaluate the Riemann sum with n = 6, taking the sample points to be…

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Q: Use a midpoint Riemann sum with n = 200 to approximate (2x2 50x + 2)dx. Round your -2 answer to four…

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Q: Use the given graph to estimate the left Riemann sum for the given interval with the stated number…

A: Left Riemann sum

Q: Use the Riemann sum with n = 2 rectangles to approximate dr. Round to 3 decimal places.

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Q: Evaluate the Riemann sum for f(x) = x – 1, -6 <x< 4, with five subintervals, taking the sample…

A: First i I have devide the given interval into 5 sub- intervals and then take the right end points of…

Q: Evaluate the Riemann sum for f(x) = 3 – -x, 2 < x< 14, with six subintervals, taking the sample…

A: Given: f(x) = 3 – ½ x, 2 ≤ x ≤ 14, with six subintervals.

Q: Consider the following table: 02 468 10 f(x) 45 44 4237 26 4 (a) Use a Left-hand Riemann Sum with 5…

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Q: Evaluate the Riemann Sum for f(x) = x² 0<x <2 with four equal subintervals using right-hand…

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Q: Estimate the area of the region bound by the graph of f (x) = x² + 3x and the x-axis on [2, 5] using…

A: The area under the graph of f(x)=x2+3x is to be calculated using the right-reimann sum on the…

Q: DEvaluate the Riemann sum for f(x) = x- 1, -6<x<4, with five subintervals, taking the sample points…

A: A function is given that is f(x) = x - 1. We have to find the Riemann sums for f(x) on the interval…

Q: 5. Suppose that f(x) = sin x on the interval [0,2n]. Partition the interval [0, 2n] into four…

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Q: Suppose f(x, y) = /xy and R is the rectangle with vertices (0,0), (6,0), (6,4), (0,4). In each part,…

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Q: 12 Using a right-hand Riemann sum with four subintervals estimate f (x – 4)da. 4 341 341 10 O 68 O…

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Q: By approximating the area, in square units, between the curve y = h (x) and the x-axis from x = -2…

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Q: Evaluate the Riemann sum for f(x)=3.8-x^2 over the interval [0,3] using six subintervals, taking the…

A: To find riemann sum , first we divide interval [0, 3] into six Subinterval

Q: 3. Use a midpoint Riemann sum with n = 300 to approximate (22³ – 8)dr. Round your answer to -2 four…

A: we are to divide the interval with length ∆x =0.023333333333333 So  the data points are…

Q: .5 Estimate the middle Riemann sum for 1 dx (n= 4). 3 1-lnx

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Q: use linear approximation to estimate the given number L( x) =f(a) +f'(a )(x-a)(2.003)^4IF…

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Q: use the given graph to estimate the left Riemann sum for the given interval with the stated number…

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Q: (a) Find an approximation to the integral  ∫04      (x2 -3x) dxusing a Riemann sum with right…

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Q: b. Using right Riemann sums with 5 subintervals, approximate the net area bounded by the function…

A: We have to divide [-4,6] into 5 subintervals.  So each interval is of width= (6-(-4))/5= 2 So the…

Q: A heavy rope, 40 ft long, weighs 0.3 lb/ft and hangs over the edge of a building 90 ft high. (Let x…

A: Our aim is to find the work  done(W) in pulling half the rope to the top of the building.

Q: 7. Write down and evaluate a Riemann sum with 4 terms that gives an upper estimate for 8 SZ+1 -dx.…

A: Given, ∫08x+1x+2dx

Q: IF F(X)=2x^2-2x on(-4,2) find the riemann sum with n=3 subintervals taking the sample points to be…

A: Given function is  We will divide the interval [-4,2] into 3 subintervals , the length of each…

Q: Evaluate the Riemann sum for f(x)  =3 -1/2x , 2 ≤ x ≤14 ,with six subintervals, taking the sample…

A: Given that, The formula to find left Riemann sum: Where x0, x1, x2 , ..., xn-1 are the left…

Q: What is a Riemann sum? Why might you want to consider such a sum?

A: a) A Riemann Sum is a method for approximating the total area underneath a curve on a graph,…

Q: Suppose that f (x) = sin x on the interval [0, 2n]. Partition the interval [0, 2n] into four…

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Q: evaluate the Riemann Sum for f(x)=x-1, -6 less than or equal to x less than or equal to 4, with five…

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Q: What is the Riemann sum of f(x) over [2,10]with n-4 partitions and mid-points for sample points?

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Q: Based on the table, use a left Riemann sum with sub-intervals given by the table to estimate the…

A: The Riemann method to calculate area divides the area into sub-intervals. These sub-intervals…

Q: If f(x) 2x - 7,0 < x< 3, evaluate the Riemann sum with n = 6, taking the sample points to be…

A: Given function fx=2x2-7, 0≤x≤3 The objective is to evaluate the integral ∫032x2-7dx with n=6 using…

Q: Evaluate the Riemann sum for f(x) = 3x - 1, -6 sxs 4, with five subintervals, taking the sample…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.