Estimate the area under the graph of f(x)= 7 +4x^2 from x = -1 to x = 2 using both three rectangles and six rectangles with left, right, and middle endpoints

Q: Estimate the area under the graph of f(x)=x^2+4x+9over the interval [0,7][0,7] using ten…

A: Given function :

Q: Estimate the area under the graph of f(x) = 9 – x° over the interval [ – 2, 1] using ten…

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Q: estimate the area under the graph f(x)=2x2+1   from x=0 to x=2 use four rectangle and the right…

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Q: 2. To approximate the area under the graph of f(x)=x'+3x +2 for -45xs1, find the sum of the areas of…

A: ∫abf(x)dx≈∆xf(x0)+f(x1)+.......+f(xn-2)+f(xn-1)∆x=b-an, n=number of rectangles

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

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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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Q: Use finite approximations to estimate the area under the graph of the function f (X) = x³ between x…

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

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Q: Estimate the area under the graph of f(x)=1/x from x=1 to x=2 using left and right endpoints.

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Q: Describe the Mean Value Theorem for Integrals in your own words?

A: The mean value theorem for integrals declares that somewhere between the circumscribed and inscribed…

Q: Estimate the area under the graph of the function

A: Given,            f(x)=x+4,   x=-3, to x=3.

Q: Estimate the area under the graph of f(x)=1/(x2+2)   over the interval [3,7]using five approximating…

A: Given: f(x)=1/(x2+2)  over interval [a,b]=[3,7] and n=5

Q: Estimate the area under the graph of f(x) = x° between x = 0 and x = 4 using each finite…

A: Given,  f(x)=x3 and a=0 and b=4

Q: Estimate the area under the graph of f(x) = 3/x from x = 1 to x = 2 using four approximating…

A: We need to divide [1,2] in 4 equal intervals. Width of each interval=(2-1)/4=0.25 So the partition…

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,…

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

A: Given, The area under the graph of f(x) using the left Riemann sum is given by where,

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…

A: The Given function is, f(x)=3-x2-2x  Between x=-3 and x=1 Here we have to find the area under the…

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 .

Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

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

A: To find:- Estimate area between the x Axis and graph of f(x) = 9-x2 ove  interval [-2, 1] using…

Q: Approximate the area bounded by the graph of Ax) = -x² + 9, the x-axis, and the vertical lines and…

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Q: Find the area between the graphs of y=8x-x+7 and y 3x -x+ 12

A: The given problem is to find the area between the given graphs. Given functions y=8x2-x+7 and…

Q: Find the total area between y = -x2 - 2x and the x-axis for -3 sxS2.

A: The objective is to find the total area.

Q: Find the area bounded by y = 5 + 2x -x2 and the chord passing through (-2, -3) and (3, 2). Sketch…

A: Let us consider two curves f(x) and g(x) [continuous functions] such that f(x)≥g(x) in the interval…

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

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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: With the use of examples, differentiate between horizontal integration and vertical integration.

A: Here , we have to differentiate between horizontal integration and vertical integration

Q: Estimate the area under the graph of f(x)=x^2+2x from x=2 to x=10 using 4 approximating rectangles…

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Q: f(x) = 3 + 2x2 from x = −1 to

A: Given: f(x)=3+2x2 from -1, 2

Q: Estimate the area under the graph of f(x)=x^2+2x from x=5 to x=11 using 3 approximating rectangles…

A: Given: f(x)=x^2+2x and 5 ≤ x ≤ 11

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

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Q: Use left endpoints and 6 rectangles to find the approximation of the area of the region between the…

A: Let's find.

Q: Estimate the area under the graph of f(x)=5 root x from x=0 to x=4 using four approximating…

A: a = 0; b = 4; n = 4; Width = Δx = (b - a) / n = (4 - 0) / 4 = 1

Q: Estimate the area under the graph of f(x) = x² – 2x + 5 over the interval (0, 7 using ten…

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Q: Use trapezoidal rule to estimate the the int 4dx n=6

A: Here we have to use the trapezoidal rule to estimate the integral.  We have,

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

A:

Q: The area bounded by the curves: у-х, у-6-х аnd у-0.5х is:

A: see below the answer and explanation

Q: Estimate the area under the graph of f(x) = over the interval [– 3, 0] using four x + 4…

A: The function is given as, fx=1x+4 It is also given that, Number of rectangles, n=4Upper limit,…

Q: Find the area of the region bounded by the graph of f(x) = x(x + 2)(x - 1) and the x-axis on the…

A: Area of the region bounded by f(x) and x- axis

Q: Estimate the area under the graph of ƒ(x) = 1/x​ from x = 1 to x = 2, first using 4 approximating…

A: Hey, since there are multiple subparts posted, we will answer the first question. If you want any…

Q: 6. Find the area bounded by the curves of y = 6x + x² andy = -x² - 2x, and the linex = 5.

A: The equation of the curves are  C1: y = 6x+x2C2: y = -x2-2xC3: x = 5 To evaluate: The area of the…

Q: Estimate the area under the graph of f(x)=1x+2 over the interval [2,6] using ten approximating…

A:

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

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Q: The area of the region bounded by the function f(x) = + 3, lines x = −2, x = 2 and the x — axis is…

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

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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: 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…

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.