f(x)=32-2x^2, over the interval [1,4]. Approximate the area between the graph of f (x) and the x-axis over the given interval by summing the area of ​​the given number of rectangles and the given condition for finding the height of each rectangle. Make sure to draw each rectangle on the graph. a)Use n = 6 rectangles and use the LEFT end of each sub-interval for the height. b)Use n = 6 rectangles and use the RIGHT end of each sub-interval for the height. c)Use n = 12 rectangles and use the LEFT end of each sub-interval for the height. d)Use n = 12 rectangles and use the RIGHT end of each sub-interval for the height.

Q: What is the total area between f(x)=6x+6 and the x-axis over the interval [−6,3]?

A: To calculate the total area bounded between the curve f(x)=6x+6 and x-axis over the interval [-6,3].…

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A:

Q: Find the approximate area between the curve Ax) = -2x + 32x + 5 and the x-axis on the interval [0,…

A: The given data is:   To find the approximate area.

Q: stimate the area under the graph of f(x)=16-x^2 over the interval [-3,2] using four approximating…

A:

Q: Find the area of the region lying under the graph of f(x) = quad root of x from x = 1 to x = 16.

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A:

Q: Estimate the area under the graph of f(x)=√x+2 over the interval [ - 2, 0] using eight approximating…

A: To estimate the area under the graph of fx=x+2 over the interval -2, 0 by using eight approximating…

Q: Find the maximum value of f(x) = 6x +1 - x on the horizontal span of 0 to 6. (Round your answer to…

A: Just use second derivative test.

Q: Estimate the area under the graph of f(x)=1/x+3 over the interval [-1,2] using ten approximating…

A:

Q: Use finite approximations to estimate the area under the graph of the function f(x) = x² + 1 between…

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Q: Estimate the area under the graph of f(x)=x^2+4x from x=4 to x=7 using 3 approximating rectangles…

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Q: Estimate the area under the graph (sqr-root):x+4 over the interval [-4,12] using 8 approxiamating…

A: Given function: Width of each interval = (12-(-4))/8= 16/8= 2  So the partition is -4, -2, 0, 2, 4,…

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A:

Q: Approximate the area under the graph of ƒ(x) = 2x + 3 and above the x-axis from x = 0 to x = 4 using…

A:

Q: What is the total area between f(x)=2x−7 and the x-axis over the interval [0,5]?

A:

Q: Estimate the area under the graph of f(x) = x² + 3x +1 over the interval [3, 5] using five…

A:

Q: Estimate the area under the graph of f(x)=x^2+4x from x=1 to x=5 using 4 approximating rectangles…

A: The given graph of the function is f (x) = x^2+4x from x = 1 to x = 5.The number of triangles is…

Q: Use finite approximations to estimate the area under the graph of the function f(x)=3−x2−2x between…

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Q: Estimate the area between the graph of F(x) = 10x2 - 7 from x = 1 to x = 7 using three rectangles…

A: We have to find the area using left end sum .

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A:

Q: Estimate the area under the graph of f(x)= 7 +4x^2 from x = -1 to x = 2 using both three rectangles…

A: All the Riemann sum are given as follows:

Q: Estimate the area between the x-axis and the graph of f(x) = 9- x over the interval -2, 1] by using…

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Q: Estimate the area under the graph of f(x) = 2x between x= 0 and x = 8 using each finite…

A: Width of the interval [0,8] is (8-0)=8For two subintervals , width of each interval=82=4So the…

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A:

Q: Using left endpoints, approximate the area under the curve of f(x) =3x^(2) + 1 over the interval [0,…

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Q: Estimate the area under the graph f(x) = x2 between x = 0 and x = 2 using left sum with two…

A:

Q: Find the total area between f(x)=3x2-3 and the x-axis on the interval [-2,2]

A: Calculation:The given curve are f(x) = 3x2 – 3 and the x axis y = 0 on the interval [– 2, 2].The…

Q: f(x) = 3 + 2x2 from x = −1 to

A: Given: f(x)=3+2x2 from -1, 2

Q: (A) Estimate the area under the graph of f(x) = 3x³ + 4 from * = -1 to z = 4, first using 5…

A: Sol: Since Using Right end point and Left end point , correct value is calculated Now Part (C) Using…

Q: estimate the area under the graph of f(x)=x^2-3x-4 from x=5 to x=13 using four rectangles and…

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Q: Estimate the area under the graph f(x)=1/(x+3) Over the interval (-2,1) Using 8 approximating…

A:

Q: Estimate the area under the graph of f(x)=x+4 over the interval [-4,4] using eight approximating…

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Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of f and…

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Q: Estimate the area under the graph of f(x)=1/(x+3) Over the interval (-2,1) using 8 approximating…

A: Given question:- Estimate the area under the graph of f(x)=1/(x+3) Over the interval (-2,1) using 8…

Q: The region Renclosed between the graph of the function y = x2 – 4x + 5 and the x-axis for 0 < x < 4…

A:

Q: Approximate the area under the graph of f(x) = 0.7x3+7x2-0.7x-7 over the interval [ -7,-2 ] using 5…

A:

Q: Use the midpoint rule with 4 rectangles to approximate the area under f(x)=x2 over [2,4]. Give your…

A:

Q: Find the area under the curve 4x2-3x+6 between x= -2 and x=3

A:

Q: Estimate the area under the graph f(x) = x2 between x = 0 and x = 4 using right sum with two…

A:

Q: Estimate the area under the graph of f(x) = x + 3x +1 over the interval [2, 4] using eight…

A: Given function fx=x2+3x+1 over interval [2, 4] and number of sub intervals, n=8. ∆x=b-an=4-28∆x=14…

Q: What is the total area between f(x)=−2x−6 and the x-axis over the interval [−8,4]?

A: The area under a curve is the area between a curve f(x) and  the x -axis is the interval [a,b] given…

Q: Estimate the area under the graph of f(x)=36−x2f(x)=36-x2 over the interval [−5,2] using five…

A:

Q: Let f(x)= 3+2x2 Estimate the area under the graph of f, the x-axis, and the lines x = −1 and x = 2…

A:

Q: Let f(x) = 3 + 2x2 Estimate the area under the graph of f, the x-axis, and the lines x = −1 and x =…

A: We have to find the area using 3 rectangle and 6 rectangle

Q: Estimate the area under the graph of f(x) = 7 + 4x^2 from x = -1 to x = 2 using three rectangles and…

A: Estimate the area under the graph of f(x) = 7 + 4x^2 from x = -1 to x = 2 using three rectangles and…

Q: Estimate the area under the graph of f(x)=√x+3 over the interval [−3,1] using eight approximating…

A: Given :  Function f(x) = √(x+3), Interval [-3,1], To find : Area under the graph of given function…

Q: Estimate the area under the graph of f, the x-axis, and the lines x = −1 and x = 2 using three…

A: In this question, we have to find the area bounded by the given curves. We need to approximate the…

Q: Use the Midpoint Rule to estimate the integral. n=4

A: Since we have been given up the integral ∫191xdxOur aim is to estimate the integral till n=4 using…

Q: Approximate the area under the graph of F(x) = x + 10x2 subintervals. Use the left endpoints to find…

A:

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.