(a) Estimate the area under the graph of  f(x) = 4 + 4x2 from x = −1 to x = 2 using three rectangles and right endpoints. R3 =  Then improve your estimate by using six rectangles. R6 =    (B) Repeat part a using left endpoints L3= L6=    (c) Repeat part a using midpoints M3= M6=

Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: Find the area bounded by the parabolas x2+y-9=0 and x2-8y=0   (SOLVE BY USING INTEGRAL CALCULUS)

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Q: (A) Estimate the area under the graph of f(x) = 3x + 4 %3D from æ = -1 to r = 4, first using 5…

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Q: 3 Estimate x dx using right endpoints for n = 4 approximating rectangles. x² dx is approximately

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Q: Find the total area between the graph of f(x)=x2−5 and the​ x-axis from x=0 to x=6.

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Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x² over the interval [-1, 2] by…

A: Clearly the given integral can be approximated by the areas of the given triangles.

Q: (A) Estimate the area under the graph of f(x) = 2x' + 3 %3D from x = -1 to x = 4, first using 5…

A: We can solve this using formulas

Q: Find the area of the region between the curve and the x-axis. In 4 3x f(x) = e - 4 from 0 to 3

A: By using area formula, we calculate the required area of the region.

Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: b. Approximate the area bounded by f(x)=x² - 2x+6 on the x-interval [0,3] usingn = 3 rectangles and…

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Q: "In Computing the area between two curves, why does f(x) have to be greater than g(x) over the…

A: In computing the area between two curves, why does f(x) have to be greater than g(x) over the…

Q: Find the total area between the curve of the function f(z) = -4z +8 and the z-axis over the interval…

A: I have provided solution in  step2.

Q: The area under the graph of f(x) = 3x2 between x = 2 and x = k is 208, where k> 2. Find the value of…

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Q: Find the area enclosed between the function f (x)=(4x2 -9)Ln (x) and the x-axis

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Q: Find the total area bounded by the x-axis and the curve f(x) = x2 + 3x - 4 over the interval [0, 4]…

A: The given curve is,

Q: Consider the region bounded above by f(x)=7x2+3x−45 and below by g(x)=8x2+22x+45. Find the area, in…

A: First, we need to find the points of interesection of f(x)=7x2+3x−45 and g(x)=8x2+22x+45At points of…

Q: (a) Estimate the area under the graph of f(x) = 7 + 2x2 from x = -1 to x = 2 using three rectangles…

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Q: Find the area under the graph of f(x) = 3x2, above the x-axis, and between x = 0 and x = 2.

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Q: Find the total area between the curve of the function f(x)=−4x+8 and the x-axis over the interval…

A: To find the total area between the curve of the function f(x)=−4x+8 and the x-axis over the interval…

Q: Consider the region bounded above by f(x)=7x2+3x−45 and below by g(x)=8x2+22x+45. Find the area, in…

A: The given functions are,

Q: For the area under the curve f(x) = x(x+1)(x+7) above the x-axis, and between the vertical lines…

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

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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: Consider the region bounded above by f(x)=−2x3−9x2−10 and below by g(x)=−x3−12x2−10. Find the area,…

A: To calculate the area contained between the two given curves (as boundaries)

Q: Find the area bounded by the loop of the curve y² = 4x²-x*

A: The given equation of the curve is: This can also be written as: The graph of this curve is:

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: (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: Find the total area between the curve of the function f(x)=2x+4 and the x-axis over the interval…

A: We have to find the total area under f(x)=2x+4 and the x-axis over the interval [−9,−1]Recall that…

Q: Question in image along with part (a) repeated using left points and midpoints.

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Q: (a) Estimate the area under the graph of f(x) = 9 + 2x from x = -1 to x = 2 using three rectangles…

A: ∫abf(x)dx≈Δx(fx1+f(x2)+....+f(xn-1)+f(xn)) where Δx=b−an.  We have that f(x)=2x2+9, a=−1, b=2, and…

Q: A cylindrical can, open at the top, is to hold 160 cm³ of liquid. Find the height and radius that…

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Q: 4.1 Can you show me all the steps to solve problem 5?

A: (a) Draw the graph for the function with three rectangles using the right endpoints as shown in…

Q: Estimate the area under the graph of  f(x) = 4 + 4x2 from x = −1 to x = 2 using three rectangles and…

A: In this question, we find the area by using the midpoint rule for the given function f(x)=4+4x2 for…

Q: ii, Find the area under the graph y=5x4 between the limits x= 1 and x-3.

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Q: Example: Find the area of the region in the first quadrant that is bounded above by Y1 =Vx and below…

A: The graph is shown below:

Q: The total area bounded by the graph of y =r 2. 1 and the x-axis is represented by

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Q: Can i get help step by step with this problem please

A: It is given that f(x) = 5x2, x0 = 0 and xn=2.(i)

Q: Find the total area bounded by the graph of y = x² + 2x and the x-axis on [-2, 2).

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Q: (a) Estimate the area under the graph of f(x) = 7 + 2x² from x = -1 to x = 2 using three rectangles…

A: We have to estimate the area under the graph of f(x) = 7 + 2x^2 from x = -1 to x = 2 using three…

Q: Q1: The area of the region bounded by the graph of y=-0.5x+4and y=3x in first quarter.

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Q: Find the total area bounded by the graph of y = x² + 2x and the x-axis on [-2,2].

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Q: Find the area the region lying between the x axis and the curve y=(ln(8x)-1)/x2 to the right of the…

A: Given curve is y=ln(8x)-1x2 Since region lying between x-axis and the curve to the right of the line…

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

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Q: A factory selling cell phones has a marginal cost function C(x)=0.01x2−3x+229 where xx represents…

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Q: 14. (a) Find the area bounded by the curves y = 2x² and y = 4x. %3D (b) Two cars both start on a…

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Q: Find the area (sq. units) covered by the line y = -Gx+ 3) from x1 = -8 to x2 = 0.

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Q: Find the area between the curves f(x) = x^2 - 4x +12 and g(x) = x^2 - 2x + 2  for 0 ≤ x ≤ 3

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Q: Find the area bounded by the curve f(x) = x³ + 3x² – 4x – 5 and x-axis from x = -3 to x = -1 using:…

A: Consider the given area bounded by the curves as y=x3+3x2-4x-5 and the x axis from x=-3 to x=-1. Let…