Find the area bounded by the curve y=10+4x+x^2 and x-axis from x=-3 to x=-1.

Q: Find the area bounded by the parabola y^2=4x and the line 2x-4. (with graph)

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Q: y = ln x and x - y -4 = 0

A: Explanation of the answer is as follows

Q: By integration, determine the area bounded by the curves y = 6x – x ^2and y = x^2 – 2x.

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Q: Determine the area bounded by the curves y=sinhx, y=coshx, the y-axis and the line y=1.

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Q: stimate the area under the curve  -(x)2+

A: Here we have to find the area under the curve -x2+1 with an interval of 0,14.

Q: Find the area between the curves.

A: First sketch the region bounded by the curves x=1,  x=6,  y=1x  and  y=12 as shown below.

Q: . Find the area bounded by the curve f(x) = (2+x)(x – 5), the lines = -2, line = 0 and the x - axis.

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Q: Find the area between the curves. x = -3, x = 0, y = 1 -x2, y = 0

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Q: Find the area bounded by the indicated curves. y = x4 - 18x? + 81, y = 81 - x

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Q: Determine the area bounded by the curves y = -x² – 18x + 63 and y = (x – 3)². |

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Q: Find the area bounded by the curve: y = 8x – x² and y = 3x

A: a) Consider

Q: Determine the area bounded by the curves y = -x – 18x + 40 and y = (x - 2)2

A: The x coordinates for the points of intersection of the curves are given by:…

Q: Find the area of the region that lies under the curve y = 4x-x over the interval 0<x<4. y = 4x - x

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Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4 and provide a correct and…

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Q: Find the area of the region bounded by the curve y=x²-3x²-x+3 and x-axis from x=-1 to x=2. (Note:…

A: To find the area of the region bounded by the curve y=x3-3x2-x+3 and x‐axis from x=-1 to x=2.

Q: Find the area of the region bounded by y = 10x + 4, y = -10x + 3 and x = 14. Leave your answer…

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Q: Find the area of the region bounded by the curve y = 9 - x2 and the x-axis.

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Q: Find the area bounded by the curve y = 4+2x+z² and x-axis from z=-3 to z = -1. Area of the region -

A: Given query is to find the area of the region bounded by y=4+2x+x2  and x-axis from x=-3 to x=-1

Q: Find the area bounded by the curve y = 9 – x2 and the x-axis.

A: Area

Q: FInd the area bounded by the give curves y=6x2-8x-2 and y= 3x2+4x-11

A:

Q: Determine the area bounded by the curve y = 2x - x^2 + 5 and the line joining the points (3,2) and…

A: Please see the explanation below

Q: Find the area between the curves. x = -2, x = 1, y = 2x2 + 5, y = 0

A: Given, x=-2,x=1,y=2x2+5,y=0

Q: ded by the curve or line: y2+4x-8=0, Y

A: Given that: The equation of the curve y2 + 4x - 8 = 0. The equation of the line y = 2x.

Q: Solve the area bounded by the curve y=x^2+2 and the line y=-x, x=1 and x=-2. With graph

A:

Q: solve the area bounded by the curve y=4x-x^2 and the lines x=-2 and y=4

A: To find out the area bounded by the curves.

Q: estimate the area under the curve y=x^1/2, from x=1 to x=3 using right end point estimate

A: SolutionGiventhe curve y=x,from x=1tox=3 we need to estimate the area  under the curve y=x1/2,from…

Q: find the area bounded by the curve y=4x-x² and y=0 from x=0 to x=4

A: Topic = Area

Q: Find the enclosed area by the curve with equation y=x^2-9 and x-axis in the region[-1,2]

A:

Q: Find the area of the region bounded by the curve  y = 2x2 - x  and the line  y = x + 4  .

A: To find the area of the curve.

Q: $ find the area of region in the first quadrant bounded on the left by the y-axis, below by curve x…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: The area of the region bounded by x = /9-y', the y-axis and the line x-y in the first quadrant is:

A:

Q: Calculate the area between the curves x = 1– y² by the line x = y² – 1.

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Q: Estimate the area under the graph of f(x) = over the interval [– 3, 0] using four x + 4…

A: The function is given as, fx=1x+4 It is also given that, Number of rectangles, n=4Upper limit,…

Q: Find the area of the region enclosed between the curves y= 4 -x^2 and x=3 and x-axis within the…

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Q: Find the area between the curves.    x = - 5, x = 1, y = 10 x, y= x 2 -11

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Q: 5. x-y(2-y) and x=-y

A: The given curves are; x=y2-y and x=-y Now find the point of intersection between the given curves.…

Q: Find the area bounded by the curve y = 63xe 63x and the x-axis from x = 0 to x = 4. %3D

A: To calculate Area bounded by curve y = 63xe-63x We need to use the method of integration to…

Q: Determine the area bounded by the curves y = -r - 18z + 40 and y = (x- 2)2.

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Q: By integration, determine the area bounded by the curves y = 6x – x2 and y = x2 – 2x.

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Q: Estimate the area under the curve given by the function f(x)= ^3√x on the interval [1, 8] using 6…

A: The solution are next step

Q: Find the area of the region bounded by the curve y= 1--x² and the x-axis.

A: Given equation of the curve: y=1-19x2 To find: Area of the region bounded by the curve and x-axis.

Q: Determine the area bounded by the curve y = x2 - 3x -6 and lines y =-4-x,x = 0 and x = -2.

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Q: Estimate the area of the region under the curve        y = -x3 + 5 and above the x-axis for…

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Q: Sketch the region bounded by the line y -axis. = 2 and the graph of y = sec2 x for −π2 &lt; x &lt;…

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Q: find the area of the region bounded by the curve y=x2 - 4x+3  , x axis and the lines x=2 and x=4

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Q: Find the area of the region bounded by the curve y=1--x2 and the x-axis. 9

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Q: Find the area bounded by the curves y=x4-2x2 and y=-x2+4 at an [-1, 1].

A: The region bounded by the curves y=x4-2x2, y=-x2+4 in [-1,1] is:

Q: Find the area bounded by the curve or line: 4y = x2-2lnx, y=0, x=1, x=4

A:

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.