Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. f(x) = x² + x – 20; [2, 5]

Q: Find the area, if it exists, of the region between the curve and the x-axis on the given interval.…

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Q: 1. Find the area bounded by the parabola y=4ax, the x-axis, and the lines x=4a, x=9a.

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

A: Given:    Approximate using mid point rule:∫04x2+4x dx ,  n=4

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

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Q: Consider the function f (x) = –x² +9. What is the approximation of the net area under the curve of f…

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

A: Given, f(x) = x2, we have to find the area under the graph f(x) and above x-axis between x = 0 and x…

Q: Calculate the area, in square units, bounded above by f(x)=x2+8x+16 and g(x)=8x+80 and bounded below…

A: The solution of the problem is given in the next steps.

Q: Calculate the area, in square units, bounded above by f(x)=x2+4x+4 and g(x)=−4x+4 and bounded below…

A: Consider the curves, fx=x2+4x+4,   gx=-4x+4 To sketch the graph: Here there are two region be…

Q: Find the area bounded by the line f(x) = 2x + 9, the curve g(x) = x² 4x + 14, and the two vertical…

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Q: Consider the function f(x) = x² - 3x + 2 on [0,4], Find the total area between the curve and the…

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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: Find the area of the region bounded by the graph of f(x) = 4 − x2, the x-axis, and the vertical…

A: Given curves: The graph is:

Q: Find the area between the curves f(x) = −x² + 4x and g(x) = x² - 6x + 8.

A: Basic identities of integration are used

Q: Find the geometric area of the region bounded between the graphs of f (x), g(x) as given: f(x) = x2…

A: Sketch the graphs as shown below.

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: Q2/ Find the total area between the curve y = -x² – 2x and the X-axis.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: f(x) = 3. 2. 14

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Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. f(x) =…

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Q: Determine the area, in square units, bounded above by f(x)=−x2−8x and g(x)=3x+24 and bounded below…

A: Topic = Application of integration

Q: Find the area bounded by the line f(x)=2x+2, the curve G(x)=X^2-6X +9 and the two vertical lines X=1…

A: Given:       fx=2x+2        gx=x2-6x+9        x=1,x=5 Area bounded by line and curve is:…

Q: Determine the area, in square units, of the region bounded by g(x)=−10x+11 and f(x)=x^2−5x−13 over…

A: Solve the following

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: Find the area, if it exists, of the region between the curve and the x-axis on the given interval.…

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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 of the region bounded by the y-axis, the line x = 3, and the functions f(x) = 1/2 (x^2…

A: Consider the functions fx=12x2-3x+10 and gx=-13x-1 Find area of region bounded by the y-axis x=0 and…

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: Find the area of the region between the graphs of y = 15 – x² and y = - 3x + 5 over the interval 0 <…

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Q: If R is the region between the graphs of the functions f(x) = 4x + 9x2 + 7x – 3 and g(x) over the…

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

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Q: 1. Determine the area of f (x) = 3 + 2x – x² and above the x axis. - X - 3x 3 3 2. Determine the…

A: To find the area of f(x) and above the x-axis, use the formula, A=∫-13f(x)dx and substitute f(x)…

Q: Find the area (in square units) of the region under the graph of the function fon the interval [-1,…

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Q: find the area between f(x)=x^2-16 and the x axis from x=0 to x-=9

A: The given function is fx=x2-16 We have to find the area between fx and the x-axis from x=0 to x=9

Q: Determine the area, in square units, of the region bounded by g(x)=6x+12 and f(x)=x2 +7x−8 over the…

A: We have to find the area under the curve of g(x), then substract the area under the curve of f(x).…

Q: Find the area of the region between two curves f(x) = 3x + 1 and g(x) = x from x = 0 to x = 1.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the area between the curves f(x) = x2+2x+1 and g(x) = x+1

A: We need to find area between given curves.

Q: Find the area (in square units) of the region under the graph of the function f on the interval…

A: Given fx=9x2-6x-5        1,4

Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: (Area Under a Curve)

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Q: Calculate the area between the graph of f(x) = x² (x + 4) and the x-axis given x E [0, 5].

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Q: Given the function f(x)=−x−2, find the total area between f(x) and the x-axis over the interval…

A: To find the area of the given region which may lie both above and below the x-axis.

Q: 1. Find the exact area between the curve f (x) = 9 – x², the x-axis, and x=-3 and x=3.

A: As mentioned, use the sigma formula to find the area A. Plot the curves. Divide the area between the…

Q: Find the area bounded by the two curves f(x) = x2 – 8x + 8 and g(x) = - x² + 6x – 8, and the two…

A: The given two curves:fx=x2-8x+8 and gx=-x2+6x-8and the two vertical lines are x=3 and x=4.We need to…

Q: 4. Find the surface area of the function x when revolved around the x-axis. between x=0 and x1

A: When a curve is revolved about an axis, we obtain a surface and there are several pre-defined…

Q: Find the area, if it exists, of the region under the curve on the given interval of the x-axis. 1…

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Q: Consider the region bounded by f(x)=−x2+11x−3 and g(x)=5x+5. Find the area, in square units, between…

A: Given:

Q: Area under the curve?

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 3 – z, and the line perpendicular…

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