For the area under the curve f(x) = x(x+1)(x+7) above the x-axis, and between the vertical lines x=-1 and x=0

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: 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: Find the area between f(x)=x²-7 and the x-axis from x = 0 and x = 6. ...

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Q: Find the area between the curves. y = x2 − 2x + 7 and y = x2 + 8 from x = 0 to x=6

A: Let fx=y=x2-2x+7 and gx=y=x2+8. First, we will find the intersection point of both the curves…

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: Consider the region bounded above by f(x)=−6x^2−50 and below by g(x)=−5x^2−19x+40. Find the area, in…

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

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Q: Estimate the area between the x-axis and the graph of f(x)=9−x2f(x)=9-x2 over the interval…

A: We will use rectangle's formula to evaluate the area of curve

Q: Find the total areas of the regions a. Between the graph of f(x) = 1- Vx and the x-axis for 0 < x <…

A: Given:        fx=1-x interval 0≤x≤4  Total area of the region between the curve fx and the x-axis…

Q: Determine the area to the left of g(y) = 3-y2 and to the right of x = -1

A: Area

Q: Find the area bounded above the graph of the function f(x) = 9-x2 /4 and below the graph of the…

A: We first sketch the region using a graphing calculator.  The x coordinates of the intersecting…

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

A: function f(x)=4-x2 To find area of region bounded by f(x), x-axis and the line x=1 and x=2.

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: Determine the area, in square units, bounded above by f(x)=−x^2−8x and g(x)=3x+24 and bounded below…

A: Given that  fx=−x2−8xgx=3x+24 To find the area bounded above by f(x)

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

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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…

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Q: The area under the curve y = 2x bounded from below bythe x-axis and on the right by x = 4 is 16 3…

A: Given that the area under the curve y=2xwe need find the area below the x-axis and the right by x=4

Q: The area under the curve y = Vĩ bounded from below by the 16 x-axis and on the right by x = 4 is…

A: Integration can be used to find area of region bounded by a set of functions. For two functions…

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: Find the area of the region in the xy-plane bounded above by the graph of the function f(x)=9, below…

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Q: What is the area of the region bounded by the curves y=f(x)=x3-4x2+5x and y=g(x)=3x-x2 between x=0…

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Q: The area bounded by the curve y = 14.x and the lines x = 4 and x = 6 above the x- axis is 364 square…

A: Area=∫ab(upper curve-lower curve)dx∫xndx=xn+1n+1+C

Q: The area between the curve y = = and the x-axis from x = 10 to x = 20 is the same as the area…

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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: 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: The region bounded by f(x) = (x + 1)-³ and the x-axis on the interval [0, ∞) is revolved about the…

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Q: Find the area of the region in the xy-plane bounded above by the graph of the function…

A: Given  fx=711x-2111, x=3 &amp; x=14 To find Area:

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 bounded by the function f(x) equals .3x^3-1.5x^2+19 the X axis and the lines X=2 and…

A: We will find out the area under the curve.

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 bounded by f(x)=X^2-4X +3 the X axis in the lines X=2 and x=6

A: We will find out the area of the region.

Q: The area bounded by the curves y = 1 -x2 and y = - x2 + 2 x + 3 , line x = -1 and x = 1 is

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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: Given the graph of the function :

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

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Q: 18: Find the total area of the region between the functior F(x) = x3 – 4x² + 3x and x-axis from…

A: The given curve is we have to find the area bounded by the region f(x)  and x-axis from [-3,3].

Q: find the area between y=2x2+9x-5 and y=-X2+6x+1 for x in (-2,2)

A: The given curves are,

Q: - Find the total area between y = x/3- x and the x-axis for -1 sx< 8. %3D

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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 of the region completely enclosed by the graphs of the functions: f(x)=x^3-8x+3 and…

A: fx=x3-8x+3 gx=x+3 find the intersection points x3-8x+3=x+3 x3-8x+3-x-3=0 x3-9x=0 xx2-9=0 xx+3x-3=0…

Q: find the area of the region bounded by the graphs of f(x)-2x2-6x+5 and g(x)=x2+6x-15.

A: To find the area of the region bounded by the graphs of fx=2x2-6x+5, and, gx=x2+6x-15.

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.