Consider the area under f(x)= x² +1 on the interval [-2, 3]. (a) Compute R5, the Righthand Approximation using 5 subintervals. Show all steps. (b) Set up the complete sigma notation for Rn (n subintervals); the only variable present should be k (since n is constant). (C) Evaluate the sum and take the- limit.

Q: Evaluate the right sum for the definite integral V4x+1 dx using the subdivision of the interval [0,…

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Q: 3 Evaluate :/ (x +3) dx using the limit of the Riemann sum with n partitions using right endpoint…

A: The integral is given as, ∫13x2+3dx Here, a=1b=3fx=x2+3 According to the Reimann Sum Method,…

Q: Approximate the area under the curve y=1x between x=1 and x=5 using the Trapezoidal Rule with n=4…

A: Width of each interval = (5-1)/4= 4/4=1 So the partitions are 1, 2, 3, 4, 5

Q: Find the area bounded by the curve y and its asymptote/s. (1+x2)

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Q: Use the limit process to find the area of the region bounded by the graph of the function and the…

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Q: Find the exact area of the region under the graph of y= e -x from 0 to 2 by using a computer algebra…

A: We have given a function; y= e -x We have to find the area of the bounded region from 0 to 2.

Q: 2. a) Estimate the area bounded by the curve and the x-axis on [1, 6] using the 5 equal subintervals…

A: As per our guidelines, we are supposed to solve only first subpart. Kindly repost other subparts as…

Q: Find the area under the graph of the function y=2-x-x² over the interval [-2,1].

A: Given query is to find the area under the curve.

Q: Approximate the area under the curve f (x) = x + x² over the interval [0,4] with n subintervals.

A: Approximate the area under the curve f(x)=x+x^2 over the interval[0,4]

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,…

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Q: 3. Approximate the area under the curve y =x² +2 between x = 1 and x=7 using 3 subintervals (n = 3)…

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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: Find the area A of the region R between the graph of f(x)= (x^2)/(4-x^2)^(1/2) and the x-axis on the…

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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: 6, find a formula for R, on the interval [1, 3] Given f(x) = 4x² - Rn Now compute the area under the…

A:

Q: 16. Between f (x)=x +2x and the x-axis on [3,4].

A: we have to use the limit process to find the area of the region between fx=x2+2x and the x axis on…

Q: Let f(x) = x2     Using the rectangle sum method, estimate the area under the curve for the interval…

A:

Q: Approximate the area between f(x) = x+2 and the x-axis from x 1 to x 7 using a trapezoidal sum with…

A: fx=x2+2,  x=1 ,  x=7,  n=3. Here, h=b-an⇒h=7-13⇒h=2 Therefore the subintervals is, 1, 3, 3, 5, 5, 7…

Q: The area under the graph of y =√2x^2 + 3 over [2, 7] using rieman sum

A:

Q: Use the Comparison Test to determine for what values of p the integral dx converges. xP In(x)

A: Comparison Test: - For any two function f(x) and g(x) which satisfies 0≤f(x)≤g(x) on interval b,∞ if…

Q: Find a formula for the area function of f (x) = 2x + 4 with lower limit a = 0.

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Q: 4. Use a right-sum and left-sum, with 4 subintervals each, to estimate the area under the curve of y…

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Q: 1/8 | x In (8x)dx

A: To find the value of integral substitute 8x=t

Q: Use a Riemann sum to approximate the area under the graph of f(x)=2x3  on the interval 2≤x≤4 using…

A:

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…

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Q: Find the area under the curve y = 6x° over the interval [0, 2]|

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Q: Estimate the area under f(x)=x2 on the interval [0,10] using the midpoint Riemann Sum for n=5.

A:

Q: 2. Use left and right Riemann sums to determine the area under the graph of y = -r² + 4x – 3 for 1…

A: Solution is given below:

Q: Approximate the area under the curve over the specified interval by using the indicated number of…

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Q: Use a Riemann sum to approximate the area under the graph of f(x)=2e−x on the interval 1≤x≤2 using…

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Q: (C)8. Approximate the area under y = 3-х between the interval 1 < x < 4 using a left Riemann sum…

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Q: Find the area under the curve f(x) = 3x+ 1 over the interval [2, 6] with n = 4 by using right end…

A: Given f(x)=3x+1, a=2, b=6, and n=4.

Q: f(x) = 8ln(x) – x

A:

Q: What is the area beneath the curve y=x2 +1 and above the x-axis from x = 0 to x = 4 by using the…

A: Here we have to use Riemann right end sum

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

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Q: 8. Find the area in the first quadrant bounded by x = 0 using the most y=x², y = 2-x and appropriate…

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Q: The function f(x)=4e^x is defined over the interval [-2,3]. Appproximate the area A by partitioning…

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Q: Approximate the area of the region between the graph of the function g(x)=36x−x3g(x)=36x−x3 and the…

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Q: (a) Estimate the area under the graph of f (x) = x² + 1 from x = 2 to x = 4 using four subintervals…

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Q: Q1/ Find the area of the region bounded by the given curve (y = x² - 5) and the curve (x = -) by…

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Q: Approximate the area under the curve y=3x between x=−2 and x=2 using Simpson’s Rule with n=4…

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Q: Use the Comparison Test to determine for what values of p the integral 1 dx converges. xP In(x)

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Q: 4 Estimate the area between the function y = + 3 and the a-axis on the interval [3, 7] using 4…

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Q: Determine the exact area of the region bound by the graph of f (x) = –x² + 5 and the x-axis on [-1,…

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Q: Evaluate the integral x°dx by taking the limit of the аppropriate Riemann sum.

A: Riemann sum: by the definition of the definite integral

Q: - Use the midpoint sum formula to calculate the area under the curve f(x) = x³ from x=0 to x-12…

A: Here h = b-an = 12-04 = 3

Q: Find the left-endpoint approximation for the area under the curve f(x) = x2 on the interval [0, 2]…

A: Given

Q: Using the right-hand endpoint with n = 8 to write the Riemann Sum that describes the estimation of…

A: Given: n = 8 f(x) = x2 + 1

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.