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

Q: Find the area of a region bounded by the curves y=e^(2x) - x^3 , the y-axis and x=1

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Q: Draw the graphs and find the between the area curves f (x) = (-1)**'x² + (-1)**' (b+3)x+(-1)°(c+5)…

A: This problem is an application of Definite Integrals and I find the area enclosed between the curves…

Q: Determine the graph of the area between the curves bounded by y = -x² + 1 and x=y A B C D

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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: 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: (b) Find the area enclosed by the curve y = 4x2 and the x-axis between x = -2 and x = 2. %3D

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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: Sketch the curve and find the total area between the curve and the Given interval on the x axis…

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Q: For the area enclosed between the curves of the equation f (x) = x and g (x) = k to be 30 (ul), a…

A: here we have to find the intersection points compare both functions  so upper and lower limit…

Q: Find the area of the "triangular" region in the first quadrant that is bounded above by the curve…

A: Given curves are y=f(x)=e^3x,y=g(x)=e^x and x=ln8.Firstly, we find point of intersection of f(x) and…

Q: Find the area between the graph of x = and the y-axis on the interval [1, 4]. 4 3 2- 1 0.5 05 1 1.5…

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Q: Find the area enclosed by the graphs of the functions y = x² + 1 and y = 1− x² + 2x. -

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Q: by the x-axis (y = 0)

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Q: Q2. Find the area enclosed by the curve y = x³ – 3x² + 2x and the x-axis.

A: To find the area enclosed byy=x3-3x2+2x and x-axis

Q: The area bounded by the curve y2=12x and the line x=3 is revolved about the line x=3. What is the…

A: The correct answer is option C. Given  y2=12x and equation of line x=3 The point at which the line…

Q: Find the area of the region bounded by y = xInx and the x-axis between x=1 and x = e

A: Using formula of Area Under The Curve.

Q: Find the area bounded by the ff. curve and line: y = xe^– x , the x-axis and the maximum ordinate

A: The curve y=xe-x, we have to find the area bounded by the curve, the x-axis and the maximum…

Q: 8 x2 = 4y and y %3D x2+4

A: We have to find the area bounded by the curves.

Q: Find the area bounded by the curve 5y2 = 16x and the curve y2 = 8x − 24 and provide a correct and…

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

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Q: Find the area bounded by the curve y = x² and the x-axis and the ordinates x = 1 and x = 3

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Q: Calculate the area, in square units, of the region bounded by the line x = 2 on the left, the curve…

A: Given that  The region bounded by the curve  fx=lnx-6+1 and the lines are x = 2, y = 3 and x-axis.…

Q: = y° and What is the area enclosed between the graphs of 1 = X2 = -3y + 4? Note: Round to the…

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Q: Find the area bounded by the ff. curves and lines: a. y = xe^–x , the x-axis and the maximum…

A: To find the are bounded by the curves and lines: (a) y=xe-x, the x-axis and the maximum ordinate.

Q: find the total area between the curve g(x)=x^3 + 2x^2 -x-2 and the x-axis, from x=0 to x=2

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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: 1. Find the area under the parabola y = 8 – x 2 – 2x, above the x-axis.

A: Given parabola y=8-x^2-2x Area = double integral (dx dy). First we will draw the graph based on…

Q: Below is the graph of y = x² +5. 141 12- 10 -2 -1 8- 6- 4- 2 0 1 2 3 The area bounded by y = x² +5…

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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 formed by the boundaries y=1, x=2, and y=e^(-x) is closest to:

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Q: 1. Find the area bounded by the curve y = x^2, the x- axis, and the ordinates x = 1 and x = 3.

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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: Find the area of the region between the curve and the​ x-axis. ​f(x)=36−x2​, from −8 to 8.

A: The function is given by fx = 36-x2;  -8≤x≤8 To evaluate : The area of the region between the curve…

Q: The total area bounded by the graph of y = 5 - x, the line a x = 0 and the x-axis

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

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Q: Find area of the region under the curve y=x^3−9 and above the x-axis, for 5≤x≤7. area=

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

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Q: 7. Find the area bounded by the curve y = x e¯** , the x-axis and the maximum ordinate.

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Q: Find the area bounded by the curve y=x^2, the axis, and the ordinates are x=1 and x=3.

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Q: Find the area between the y-axis and the graph X = /y on the interval 1, 4]. 4 3- 2- -1 0 1 2 3 O 16…

A: The given question has been solved in detail and option (c) 14/3 is the correct answer.

Q: Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. Find the value…

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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: Find the area bounded by the given curves. x2 = y - 1 and x = y - 3

A: From the given curve   x2=y-1 ; x=y-3   Now finding the point of intersection for both curves:…

Q: Find the area between the graph of y = x² – 2 and the x-axis, between x 0 and x = 4. %3D

A: Use integration to find the area.

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: Compute the area bounded by the curve y = x2 + 3, the x-axis and the ordinates x = 1; = 4.

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Q: Calculate the total area of the curve y=x' and the x-axis between x-2 and x=-2. O 8 sq units 11 sq…

A: The given bound region is: Now taking vertical elementary strip; So, the area of the strip from the…

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.