1* quadrant area of y = (4-x)/(x+2)²

Q: Estimate the area under the graph of f(x) = 9 – x° over the interval [ – 2, 1] using ten…

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Q: Does the Midpoint Rule ever give the exact area between a function and the x-axis? Explain

A: The midpoint rule is an approximate method to calculate the area between the curve and x axis. Using…

Q: FIND THE AREA BOUNDED BY THE FF CURVES AND LINES: show rough sketch of graph pls

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Q: Iwo curves having an equation of x = 2Vy and Compute the area between the two curves.

A: Given,          x=2y    and    y=2x

Q: Find the area of the bounded region by the equation y= x+4 , Y - -4 y- ayis and the x-axir.

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Q: Find the area bounded by the curve y=4x-x? and the lines x=-2 and y=4.

A: The given equation forms a downward parabola.

Q: find the area bounded by the following curves and lines  y = 3x/square root of x+4  where y = 0 and…

A: The given region are: y=3xx+4, y=0, x=4

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

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Q: 4. Find the area bounded by the curves y = 2x – x2 and the x-axis

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Q: Find the area bounded by the curves f(x) =x and g(x) =x4 ,Also sketch Graph and colour bounded area?

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Q: the area bounded by the curves y=2-x2 and y=x2 is

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Q: 7. y=- y=0, x =1, x = -1

A: We will solve for first part only. Given equations of curve: y2-6y=-xy2-2y=x

Q: Find the area bounded by: x^2 + 4x + y =0 and x + y = 0. Draw the curve and label the graph.

A: Given, x^2 + 4x + y =0 and x + y = 0.   or y=-(x2+4x) and y=-x

Q: Determine the area bounded by the curves x^3 - y = 0 and y + 3x^2 - 4 = 0 using a vertical element

A: The area is bounded by the given curves x3-y=0 and y+3x2-4=0. The main objective is to determine the…

Q: Determine the area of the region bounded by the curves y = x4 - x2 and y = x2 - 1

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Q: 1 y = 1+x? 1+. y=0, x =1, x = - 1

A: Given:              y=11+x2            y=0 , x=1 ,x=-1    Area bounded by the curve is A=∫abf(x)dx…

Q: y = 4/x, y- 4y + 2x = 5 and the line y = 4

A: Sketch the region and integrate in y variable.

Q: Determine the area bounded by the curves y = 6x − x2 and y = x2 − 2x and illustrate an accurate…

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Q: Find the area under the curve y = 3xe for æ > 3. area =

A: Given:The given curve is y=3xe-x and x≥3To find:we have to find the area under the curve

Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: I have shaded the area green which is to be calculated

Q: Find the area bounded by the curve y = 2x + x² – x³, the x-axis and lines x = 0 and x = 1. %3D

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Q: Find the area of the region bounded by the curves y = x²-2x and y= - x.

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Q: Find the area between the curves:  and  y= -x2+4x+2 and y=x2

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Q: Using left endpoints, approximate the area under the curve of f(x) =3x^(2) + 1 over the interval [0,…

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Q: Find the area of teh region bounded by y=5x/x2+2, x=1, x=5, y=0. Sketch the graph

A: We graph the region using a graphing calculator.

Q: 2. Find the Area bounded by the curve y = 4-x? and the x-axis.

A: Topic = Area

Q: Find the area of the region by bounded by the graphs of y=x2+2x and y=-x+4 on the interval [-4,2]

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Q: zty xydx dz dy

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Q: Use the rectangles in each graph to approximate the area of the region bounded by y = 5/x, y = 0, x…

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Q: Find the area bounded by the curve y = x3-12 x and the x-axis. Sketch the curve indicating the area…

A: We need to find the area between the curves y=x3-12x and the x-axis or y=0First we need to find the…

Q: Find the area under the curve  y= (2x2 - 7) / (sqrt(x)) ,   16 <= x <= 20

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Q: Find the area of the region bounded by the graphs of y = (square root (x)) and y = x/2. Leave the…

A: Find the area of the region bounded by the graphs of y=x and y =x2

Q: Find the value of a and b if the curve +b) touches the x-axis at x=2 and line y=2x at the origin.…

A: Given curve is y=x(x-2)(ax+b) The curve touches x-axis at x=2 and the line y=2x at the origin. The…

Q: Sketch the graph and find the area bounded by the curves for y = 2x² and y = x² + 4

A: Given query is to find the area bounded by the curves.

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

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Q: To estimate the area under the graph on the interval [-4, 4], we use left-rectangle approximation…

A: Introduction: A sub-interval can be divided into a certain number of subintervals with equal length.…

Q: 4y = x 2 - 2lnx, y = 0, x = 1, x = 4 %D

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Q: How do I solve this problem?

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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 b0 und by Curves the y3= X-3

A: The region is bounded by y=9x2-36, y=0, x=1 and x=3

Q: Find the area bounded by the indicated curves. y=7-7x2, y 0

A: We have to find out the area enclosed by the curves

Q: y = 2x ,2 y+ 4x – 8 = 0

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Q: Find the area bounded by: y = 2x – 4 from y =−2 to y = 4. Draw the curve and label the graph.

A: Consider the given: y=2x−4Limits:y=−2,y=4−2=2x−4 x=14=2x−4 x=4

Q: 3. Find the area bounded by the curve y 4sin(2x), the x-axis, and the lines x = 0 and x =

A: We have to find the area bounded by the given curves. We will find the area by the help of…

Q: 6. у? - бу %3D - х Y2 – 2y = x %3D

A: To find the area between the curves

Q: %3D y = x²– 2x

A: Here we have to find the area bounded by the curves y=6x-x2 ............... (1) and y=x2-2x…

Q: FIND THE AREA BOUNDED BY THE FF CURVES AND LINES: The loop of y^2 = x^4 (4-x)

A: We have to find the area bounded by the loop  y2 = x4(4 - x)

Q: Find the area of the region bounded by a curve y = x^2-3 and y =5-x^2

A: Consider the provided curve, y=x2-3  and y=5-x2 Find the area of the region bounded by a curve.…

Q: Find the area bounded by the curve x = ý +2y and the line x = 3.Use horizontal strip.

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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.