find the total area of the region between the graphof ƒ and the x-axis. ƒ(x) = 1 - √x, 0 ≤ x ≤ 4

Q: Find the area of the region bounded by the graph of the function f (x) = x, the X−axis, and the…

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Q: Find the area of the region enclosed between f(x)=x^2−2x+4 and g(x)=2x^2−3x−2.

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Q: (b). Find the area of the region enclosed by the graphs of f(x)=x² -x and g(x)=2x.

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Q: Find the area of the region between the graphs of y = 20 - 2² and y=-2x - 15 over the interval 6 < x…

A: Please see the below picture for detailed solution.

Q: Find the area of the region enclosed by the graphs of f (x) = x3-x2 and g (x) = 2x

A: Given f(x) = x3 - x2   and g(x) = 2x The intersecting points of the functions are,  =&gt; x3 - x2 =…

Q: Find the area of the region enclosed between these graphs and the vertical lines x=3 and x=4.…

A: Here we used area between the two curves

Q: Find the area of the region under the graph of the function f on the interval [1, 4], f(x) = 6Vx 32…

A: We have to find area under the graph.

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: Graph the curve Y = - 2 x (x - 4)(x + 6)(x - 2) between the value of x [0, 4], then find the area of…

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

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Q: Find the area of the region bounded by the graphs ofy = x² - 4 and y =r+2. Give your answer as a…

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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 area of region f(x)=x2+4x+4 g(x)=4x+13

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Q: f (x) = x² + x – 6 - 6

A: By using area bounded by curve formula, we calculate the required area.

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A: Find the area of the region between the graph of fx=1x and the x-axis on the interval [1,9]

Q: Find the area of the region bounded by the graph of f and the x-axis on the given interval.…

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Q: Find the area of the region enclosed by f(x) and the x-axis for the given function over the…

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Q: find the area of the region under the graph of the function f on the interval [4,10]  f(x) = 8x - 5…

A: Area of trapezium

Q: Estimate the area between the x-axis and the graph of f(x) = 9 - x² over the interval [0, 3] by…

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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 area of the region bounded by the graph of f(x) = x3, the x-axis, and the vertical lines x…

A: We first sketch the region using a graphing calculator.

Q: Find the area of the region under the graph of the function f on the interval [0, 9]. f(x) = 9x -…

A: given  f(x)=ax-x2Requirid area , A= ∫0qf(x) dx A=∫0q(qx-x2) dx  = ∫0qqx - ∫0qx2dx

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 of the given region. 3. Region between f(x) = x - 4x and g(x) = x.

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Q: Find the area of the region under the graph of the function f on the interval [5, 9]. f(x)= 7/x2…

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Q: Find the area between the y-axis and the graph X = 1 on the interval 3, 6]. 7 5- 4 3 2 ++++ ++++ 54…

A: The area formed is of trapezium

Q: Find the area of the region under the graph of the function f on the interval [1, 5]. f(x) = 3x³…

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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 area of the region bounded by the graphs of f(x) = x³ – 3x + 2 and g(x) = x + 2.

A: Given functions are fx=x3-3x+2,gx=x+2. Graph the given functions as shown below. From above graph,…

Q: f (x) = x – 2x – 3

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Q: Use the left endpoint and 10 rectangles to find an approximation of the area of the region between…

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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: Find the area of the region bounded by the graphs of f(x) = 2 - x2 and g(x) = x.

A: f(x)=2-x2, g(x)=x

Q: Find the area of the region bounded by the graphs of f (x) = x³ and g (x) = x. (A) 1 c) 0.5 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: 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 of the following region bounded by the graph of f(x) = (x - 5) and the x-axis between…

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Q: Find the area of the region enclosed between f (x) = 0.1x2 + 4, g(x) = x, x = -8, and x = 4

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Q: Find the area of the region above the x-axis bounded by the function y = 4x - x2 – 3

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Q: Use the limit process to find the area of the region between the graph of the function and the…

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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 of the region between the x-axis and the graph of f (x)= x' – 4.x² + 3x, Osxs2. .

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

A: Given f(x)=x2+x-20. Find the area bounded by x-axis and f(x) on [2,5].

Q: Find the area between the y-axis and the graph X = -y + 5y – 4 on the interval [1, 4]. 3- 2- 54 3-2…

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Q: Find the area of the region lying under the graph of f(x) = √4 x from x = 1 to x = 16.

A: It is given that,                 f(x)=4x from x=1 to x=16We have to find the area of the region…

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

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Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x over the interval 0, 3 by using…

A: The given function f(x)=9-x2 over the interval [0,3]

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.