Find the area bounded by the curves y = x², y=A and x=B.

Q: The area bounded by y = e*, y = 2, and the y– axis is equal to

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Q: Find the Area bounded by the curves y² = x and x = 2y – y². %3D

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Q: find the area bounded by the curve y = (1 + x^2) / (2x^2) and the lines y = 0, x = y, and x = 2

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Q: Find the area bounded by the curves y=sinx and y=cosx and x=0, and x=pi/2

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Q: Find the area bounded by the curve y = x³ − 3x and y + 4 = 0

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Q: Find the area bounded by the given curves. y = 3x2 and y = 27…

A: Given:

Q: Find the area bounded by the given curves. y = 2x – x², y = 2x - 4 %3D I|

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Q: Find the area bounded by the curve y = x 2 and y = 2 − x 2

A: To find area bounded by the curves y=x2 and y=2-x2.

Q: Find the area bounded by y = (1 ²)² and y = 0.

A: y=(1-x2)2 and y=0

Q: Find the area bounded by the curves y= x', x = 2, and y = 0 using double integration.

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Q: Find the area between the curves. x = -1, x = 2, y = e-x, y = ex

A: Solution: Consider the given curves we have: x = -1, x = 2 andy = e-x, y = ex We have  Area =…

Q: . Calculate the area enclosed by the curves y = x² and y = Vx. %3D

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Q: Find the area bounded by the curve y²=9x and its latus rectum

A: Given equation is y2=9x the equation of parabola is of the form  y2=4axlatus rectum x=a  and…

Q: Find the area between x = y2, x - axis, x =y +2 To find the intersect points

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Q: Find the area bounded by the curve y = 4x - x² and and the lines x = 0 and y = 4. %3D Answer:

A: we can find the area between the curve and the lines by integrating the curve function through lines…

Q: Find the area bounded by the curves y= 5x and y = 15x.

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Q: Find the area bounded by the given curves. y = 8x3 + 7 and y = 8x + 7 _________ square units

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Q: Find the area enclosed by the curve y = x 2 − 3 and the line y = 2x

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Q: = Calculate the area bounded by the curves: A. y = x² and y² = X.

A: Note: Hi and thanks for your question! Unfortunately, as per our guideline, only one question should…

Q: Find the area bounded by the curves y = 1 – x² and y = 11 – 7x.

A: The curves y=1-x2 and y=11-7x. Find the points of intersection of two curves .…

Q: find the area bounded by the given curves y=8x3+7 and y=8x+7

A: Given,           The curves are y=8x3+7 and y=8x+7.

Q: Find the area bounded by the curves y=2x−x2 and x+y=0.

A: Given curve is

Q: ² = 2x, x – y = 4.

A: Topic = Application of integration

Q: Find the area bounded by the curves x 2 = y − 1 and = y − 3 .

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Q: Find the area bounded by the curves y = 6 – x² and y = 8 – 3x. 1 a) 6 1 b) -/6

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Q: Find the area bounded by the curve y=x³, x=0, y=1 is revolved about the x axis.

A: The graph of the curves is

Q: Find the area enclosed by the curve x = t – 2t, y = vt and the y-axis |

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Q: Find the Area bounded by the curves y2 = x and x = 2y – y?.

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

A: Here we have to find the area bounded by the curves, y=2x-x2 and y=x-2 .

Q: Find the area bounded by the two curves y = Vx and y = x².

A: The area between two curves f(x) and g(x) is given by A=∫abf(x)-g(x)dx f(x)=x2 and g(x)=x…

Q: find the area between the curves y=Vx and y x for

A:

Q: Find the area bounded by the parabola y=x and the straight line y = x

A: givenparabola  y=x2line y=xlet us find intersection point of these…

Q: Find the area contained by the curve y x(x – 1)(x + 1) and the x – axis.

A: Graph of the function y=x(x-1)(x+1) will be as following

Q: x = y² - 2y and x = 4y - y²

A: The given curves are; x=y2-2y and x=4y-y2 Now find the point of intersection between the given…

Q: Calculate the area bounded by the curves x=−(y2−y)/4    AND y=x

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Q: Find the area bounded by The curves/lines 4y=x-2 Inx, y=0,x=1,x=4

A: Guven curves are 4y=x2-2lnx,y=0,x=1 and x=4

Q: Find the area between the curves y = x and y = -x

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Q: Find the area bounded by the curve x = y^2 + 2y and the line x = 3

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Q: find the area bounded by curves x = (y + 1)^2 and y+1 = x^2

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Q: Find the area bounded by the curves y = x(x − 1)², y — axis, and the line y = 12.

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Q: Find the area bounded by the curve and y+ 4 = 0 y=x²-3x 3X

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Q: Find the area bounded by the curve y = x2 - 2, y = x, x = 0 and x = 3.

A: Draw the graph the integrate with in the limit to get the area bounded by the given curves.

Q: Find the area bounded by the line y = x+2 and parabola y = x².

A: We can solve this as follows:

Q: Find the area bounded by the curves. y = x2 + 1, y= 10

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Q: Find the area enclosed by the curves y=x5, y = √√x , x = x = 0, x = |c

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Q: Find the area bounded by the curve y = ex, the lines x = -1, x =1 and the x axis.

A: To find the area bounded by curve y = ex, the line x = -1, x = 1 and the x-axis

Q: Find the area bounded by the curves y=x2 and y=√x.

A: Given: The graph is drawn for the given curves as shown below,

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.