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Q: 1. Use the definition of the definite integral as the limit of a Riemann sum to evaluate - 4)² dx.

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

Q: Suppose sewage flows through an intake pipe in a sewage treatment plant at the rate of S(t) thousand…

A: Right Reimann sum

Q: Calculate the midpoint Riemann sum for f(x) = Væ on [3, 5]; n = 4

A:

Q: Compute the Riemann sum L4 for the function f(x)=2 cos x on the interval [0, 7]. Enter your answer…

A: To find the left riemann sum.

Q: It is also a Riemann sum for the definite integral | 9(x) dx where c = and g(x) = The limit of these…

A: We will use Riemann sum approximation to find required values

Q: calculate the indicated Riemann sum S5 , for the function f(x) = 29 -- 4x^2. Partition [ -1, 9 ]…

A:

Q: Find the Riemann sum of  f(x)=x^2-4x-12 on [0,6], where the partition number is n=3 and use the…

A: Given f(x)=x2-4x-12 on [0, 6], where the partition number is n=3.

Q: Q.2 - Use the Riemann sum approximations to approximate the area under the curve of y = x on the…

A:

Q: The area above the x-axis, below the graph of f(x) = between x=0 and x=2 is the limit of 1+z which…

A:

Q: what is the left and right endpoint Riemann sum for f(x)= (x^2)/11 on the interval [2,6]?

A: Given:

Q: Approximate the area under the graph of f(x) = x^2 + 2 over the interval [0, 4] with 4 subintervals…

A: From the given information, it is observed that a = 0 and b = 4 and f(x) = x2 + 2. Note that,…

Q: Compute the definite integral as the limit of Riemann sums, Verify by FTC, and using Desmos. 1) y =…

A: By Reimann sum, ∆x=b-an=4-0n=4n Again,  xi=0+i·∆x=4in Now,…

Q: Use riemann Sum obtained by dividing the interval equal [4,3] into subinter vals to compute the…

A:

Q: 2. Use left and right Riemann sums to determine the area under the graph of y = -a² + 4x – 3 for 1…

A: Given query is to find the area using Left and right reiman sum.

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: Calculate the left Riemann sum for the given function over the given interval a.) f(x) = 3x2 over…

A: left Riemman sum

Q: Use Riemann sum to evaluate the definite integral: 2 | (2x + 1)dx where n = 0.4

A: ∫abfxdx ≈Δ xfx0+x12+fx1+x22+fx2+x32+...+fxn-1+xn2,  where Δ x =…

Q: Evaluate the definite integral: x²)dx using limit of the Riemann sum.

A: Consider the provided definite integral, ∫02 2-x2dx Evaluate the provided integration using limit of…

Q: 4. The velocity of a speed boat in ft/sec at selected times is given in the table. t 10 15 20 25 30…

A: (a) Acceleration = Change in velocitychange in time

Q: (a) Find an approximation to the integral (x2 - 2x) dx using a Riemann sum with right endpoints…

A:

Q: Find the Riemann sum using R4 over the interval [0, π]. y = x² sin x

A:

Q: consider the integral 1² +5) dx 3 x a) Riemann sum using right endpoints and n=4 b) Riemann sum…

A:

Q: Find the formula for the Riemann sum obtained by dividing the interval [ – 1, 0] into n equal…

A: To find the formula for the Riemann sum by dividing the interval in n equal sub intervals. The given…

Q: Calculate the left Riemann sum for the given function over the given interval using the given value…

A: We have to find the left Riemann sun of given function.

Q: A test plane pilot flies in a straight line with strictly increasing positive velocity v(1), in…

A:

Q: Find the Riemann sum of f(x)3Vx on [4,9] with 4 subintervals and right endpoints. Round to the…

A:

Q: Calculate the left Riemann sum for the given function over the given interval using the given value…

A:

Q: Use Riemann sums and a limit to compute the exact area under the curve y = f(x) = 2x2 + 1 on the…

A:

Q: Let f(x) = -2x + 4, and compute the Riemann sum of f over the interval [1, 21 by partitioning the…

A: The answer is found in step-2.

Q: Find the Riemann sum of f(x) = V x on [4,9] with 4 subintervals and right endpoints. Round to the…

A: In the question we have to find right Riemann sum.

Q: 3. Express the given integral as the limit of a Riemann sum but do not evaluate: So (x³ - 6x) dx.

A: Solution:-

Q: Calculate the midpoint Riemann sum. 1 f(x) = on [2,7]; n = 5 %3D

A: f(x)=1x on [2,7] ; n=5

Q: Find the area of the region bounded by Z F6.png f(x) = alog,(cx – d) - the x -axis and the line x =…

A: Given: fx=alogbcx-d a=7.571, b=7, c=4 and d=6 To find: The area of the region bounded by fx, x-axis…

Q: Use Riemann Sums to calculate the area under the curve over the interval (1,3] for f(x) = x² + 2

A: By using Reimann Sums to calculate the area under the curve over the interval 1, 3 for fx=x2+2.

Q: Find the Riemann sum of f(x)=/x X on [4,9] with 4 subintervals and right endpoints. Round to the…

A:

Q: Find the Riemann sum of f(X)=Vx on [4,9] with 4 subintervals and right endpoints. Round to the…

A:

Q: Estimate the area under the graph of the function f(x) = sin(x-5) from x=5 to x=6 using a Riemann…

A: We have to find the area under the graph of the function f(x) = sin(x-5) from x=5 to x=6 using a…

Q: A cable that weighs 3 Ib/ft is used to lift 500 lb of coal up a mine shaft 400 ft deep. Find the…

A:

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

A:

Q: Use the methods of i. left Riemann Sum right Riemann Sum Second part Fundamental Theorem of Calculus…

A: Since there are multiple questions the first question is answered.Kindly repost if any particular…

Q: Find the formula for the Riemann sum obtained by dividing the interval [ - 1, 0] into n equal…

A:

Q: If f(x) = cos(x) Osxs 31/4 evaluate the Riemann sum with n = 6, taking the sample points to be left…

A: Given:- f(x) = cos(x)  , 0≤ x≤ 3π/4  To find:- Evaluate the Riemann sum with n = 6 taking the sample…

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

A:

Q: Estimate the area under the graph of the function f(x)=1/(x+5) from x=0 to x=4 using a Riemann sum…

A:

Q: Show that the midpoint Riemann sum for f(x) = x from 0 to 4 with n equal 4. subintervals is (4i-…

A: Use the formula for the midpoint Riemann sum and Substitute given function.

Q: Find the 3rd left Riemann sum of the function f(x)=cos x at [0,2]

A:

Q: Divide the interval (-1, 1] into four subinterval of equal length and compute the left-endpoints…

A:

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

A:

Q: 4. Determine the Riemann sum M, using the Midpoint Rule with n = 4 in order to approximate the…

A: According to Riemann midpoint rule:

Q: Determine the Riemann sum using L4 over the interval [-1,1]. y = 3x² - 2x + 1

A: Given function isy=3x2-2x+1_____(1)  , interval [-1,1]n=4 then,Δx=b-anΔx=1--14Δx=12

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.