f the region bounded by the curves y = x3-8x2

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: Q4. : Find the area of the region R enclosed by the curve y=x+2. Y3DX2 and the line

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Q: The area of the region bounded by y = v9 – x² , the x-axis and the line y=x in the first quadrant…

A: The area between the curves y=9-x2, y=x, x=0 :The area between curves is the area between a curve fx…

Q: Find the area of the region bounded by the curves y = e* y² = 4x - 4 between y = 1 and y = 2. and

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Q: Find the area of the region bounded by the curve y2= 4x and the lines x = 1 and x = 4. O 21/2 square…

A: Here is the solution

Q: Find the area of the region bounded by the curves: a) y=2x and y = 8 from x =-2 to x=2

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: The area of the region bounded by y = v9-x² , the x-axis and the line y3x in the first quadrant is:

A: The area of the region is calculated by the double integration, and to solve double integration we…

Q: Find b such that the line y = b divides the region bounded by the graphs of the y = 9 − |x| and y =…

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Q: (a) Find the region enclosed R by the curves y = x2 - 2x +1 and y = -x + 2x +7.

A: Let f(x) and g(x) are two continuous functions and fx ≥ gx on the  closed interval a, b. Then the…

Q: The area of the region bounded by the curves y=x and y= 20-x² is

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Q: The area of the region bounded by the curves y =x and y= 20-x² is

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Q: The area of the region bounded by the two curves y = x“ and y = 4 is

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Q: Find the area of the region between the curves y = x2 +9 and y = 10 + 2x over the interval [-1,3].

A: Here we have to find the area of the region between the curves y=x2+9 and y=10+2x over the interval…

Q: The region bounded by y = 3x – x² and y = -x %3D

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Q: The region between the graphs of y = x² and y = 3x is rotated around the line x = 3.

A: Given data:   The expression first curve is: y=x2. The expression for the second curve is: y=3x. The…

Q: R is the region between the curve y3x and the line y= 9x, for x 0.

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Q: Find the number k > 1 such that the region bounded by the curves y = 1, y = x-2, and x = k k has…

A: Given curves are y=1 and y=x-2 and interval is x=1 to x=k

Q: 2. Determine the area of the region bounded by the curve y = x³ – x2 – 2x, and а. the x-axis b. the…

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Q: The area of the region bounded by the curve y = a° – 3x? – x + 3 and y = 0 is

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Q: Find the area of the region bounded by the parabola y^2=x+3 and the line x - y = -1

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Q: Find the area of the region bounded by the curves, x = -6, x = 6, - axis and the parabola x2 – 4y –…

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Q: d the area of the region bounded by the curves y = 3x and y = x².

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

Q: Find the area of the region bounded by the lines ( y=x2 ) & (y=2+x) for xs 0.

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Q: The area of the region bounded by the two curves y = x² and y =4 is

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Q: 14. Find the area of the region bounded by these two curves: X = y' – 2y and x-y-4=0

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Q: The area of the region bounded by the curve y= x3−3x2−x+3 and y=0 is

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Q: Rotate the region bounded by y= x- 2x + 4 and y X+14 about the X- axis

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Q: b) Find the exact area of the region enclosed by the curve y = x² – 3x, the x-axis and the vertical…

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Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x –

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the area of the region bounded by the curves y = x2 -4x and x + y = 0.

A: We will use double integration to solve this

Q: Find the area of the region between the line y = 2x and the curve y = x2 + x − 2

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Q: 3. Find the area of the region enclosed by the two curves y = x² and y = -2x² + 3x.

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Q: Sketch the region bounded by the graphs of y%3= 1 and y=D4-3x, then find its area.

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Q: The area of the region bounded by the curves y = 4x? 3 22 and the lines æ = 1 and x = 5 and y is

A: Here is the solution of the given problem

Q: find the region bounded by the curves  y = sqrt(x) y=2-x x = 0

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Q: Find the area of the region bounded by = y ; x=2y²_4

A: The given functions are x=y2 and x=2y2-4 To find the area enclosed between the curves.

Q: The area of the region bounded by the curves 8x =y° and 8x = 2y+y2 -2y is

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Q: Find the area of the region bounded by the curve y = e2x - 3e* + 2 and the x-axis.

A: The region is bounded by the graph y=e2x-3ex+2 and the x-axis.

Q: Find the area of the region enclosed by the curves y = | x²- 4 | and y = 4 + x² / 2

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Q: Find the area of the region between the curves y=x2-1 and y= - 2x² +2 from x= - 1 to x=1.

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Q: Find the area of the region bounded by the curve y=x^2-3x the x-axis and the lines x = 1 and x = 2.

A: This question is based on application of integration.

Q: Find the area of the region bounded by the graph of y = 2x2 − 3x + 2 the x-axis, and the vertical…

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Q: The region bounded by the curves y=1-x^3. ,y=e^x.  And the line y=3

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Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x – 10

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Q: Find the area of the region between the curves y = x2 + 9 and y = 10 + 2x over the interval [-1,3].

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Q: 3. Find the area of the region bounded by the curve y = Vx – 1, the y - axis and the lines y=1 and…

A: Simplify the equation y=x-1 to obtain the expression of x. y=x-1y2=x-1x=y2+1 Draw the graphs…

Q: Find the area of the region bounded by one loop of the curve x2 y*(1 – y²)

A: Given:          x2=y41-y2         x=±y41-y2         x=y21-y2 The graph is symmetric about the…

Q: The area of the region bounded by the two curves y = x² and y = 9 is Square Units

A: Draw the both curve than find their intersection points and integrate in that interval.

Q: 4. Find the area of the region bounded by the parabola x=y^2 +2 and the line y=x-8 *

A: Given curves are x=y2+2, y=x-8 We have to find the area bounded by this region.

Q: The region is bounded by the curve y = 4x – x², y = 4 and the y-axis.

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.