| (f(x) – g(x)) dx still equal to the area between the graphs of f and g if f(x) > 0 but g(x) < 0? Is

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: We must integrate y = (8x-x2)-(2x) = 6x-x². The limits on the integral correspond to the smallest…

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Q: Find the area bounded by the line f(x) equals 3X -1, the curve G(x) equals X^2-6X +7 , and the two…

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Q: Find the area between the graph of y = x - 6x + 8 and the x-axis from x = 1 to x = 3.

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Q: 10. f (x) = x² + 4x + 4 Opens up/down:. Vertex: Axis of symmetry: Solution(s): y-int: Domain: Range:

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Q: Find the area beneath the curve g(x) = 8x + 3x2 from x = 5 to x = 6

A: Given function is,

Q: Q4. Find the area between curve y = x - 3x + 2 and x-axis from x =0 to x 2

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Q: 3. Find the exact area between the curve f (x) = -2x² + 12x + 7, the x-axis, and x=1 and x=5.

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

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 between the graph of f (x) = x² – 2x and the x-axis from x = -1 to x =

A:

Q: 5. Find the area between the curve y, =x² - 4x +12 and y, = x² from 0<x<4

A: Given curves are y1=x2-4x+12y2=x2 Also 0≤x≤4

Q: Consider the region bounded by g(x)=7x−6 and f(x)=x2+19x+14. Find the area, in square units, between…

A: The given two curves that bounds a region 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: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: find the area between f(x)=x2 +16 and the x-axisn from x=0 to x=8

A: To determine the area between the curve and x-axis.

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 exact area between the graphs of f (x) = 2x +1 and g (x) = 9 – x2. First find out where the…

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Q: 4. Find the area bounded by the curve a²y = x³, the x - axis, and the line x = 2a. Solve in two…

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Q: x-3 dx r³+9x +9.x

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

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Q: b) Find the area between the 2 curves f(x)=x²+4-4x and x-axes and border with the two lines = 5 &x=…

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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: Approximate the area under the curve f(x) on the closed interval [1, 3] with 5 circumscribed regular…

A: Given curve f(x)=x2+9x+10 interval 1,3. The objective is to estimate the area under the curve. Area…

Q: The area of the region between the x-axis and the carve y = e¯ -3x for x >0 is

A: Formula:For y=fx; y≥0 area between the curve y=fx, x=a,x=b and x-axisA=∫ba fxdxGiven y=e-3x

Q: Find the area between the curve y = x² + 12x + 27 and the x-axis from x = -3 to x = -1.

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Q: A factory selling cell phones has a marginal cost function C(x) = 0.01x“ – 3x + 229, where x…

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Q: (9) Evaluate the indefinite integral f X+2 dx x² + 4x 2

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Q: Find the Area below f(x) = -x² + 4x and above g(x) = x² – 6x +5 over the interval 1 siS4. 3

A: Given    fx = -x2+4x   gx = x2-6x+5Find out area in interval 1≤x≤4Area = ∫14fx-gxdx          =…

Q: Find the area between the curve y = x2 + 10x + 16 and the x-axis from x = −2 to x = 1.

A: We have limits of curve from x=-2 to x=1

Q: Find the area under the curve between x-2 and x=-1 for the curve f(x)=(7 – x²)d

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Q: 1. Sketch a region bounded by the function ƒ (x)= x+1 the x axis and two vertical lines so that the…

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

Q: 1. Solve the area bounded by the curve (x - 2)² = - ( y - 4) and the lines x=- 2 and y= 4.

A: The area bounded by the curves (x-2)2=-(y-4) ,x=-2, y=4 is as shown above.

Q: Find the area between the curve f(x) = x² +12 and the x-axis from x = 3 to x = 6. ...

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

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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: The area between y 3 x + 1 and y x2 from x = 1 to x 3 is

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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: 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 above the x-axis bounded by the function f(x) = -x2 + 2x + 3 and the x-axis.

A: Given that, f(x) = -x2 + 2x + 3 Points of intersection of f(x) with the x-axis are obtained when:…

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: (Area Under a Curve)

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Q: The area of the region bounded by the 2 curves f(x) = x² + 1 and g(x) = 2x + 1 is best described by:…

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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: 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: For the area bounded by the x-axis and the function f(x) = x² – 3x + 2, using Euler's Forward…

A: Note: We are not given number of steps for the approximation. Graphical Representation:

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01x? – 3x + 229, where x…

A: Given C(X)=0.01x2-3x+229      And R(X)=429-2x Where X is the number of cell phones

Q: 2. Find the area bounded by y = 4x – x² and the x – axis. · Solve in two ways.

A: Solution:Giveny=4x-x2   and x-axisTo find the area of the bounded region.Formula:Area=∫abydx

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: 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…