Find the area between the curves -4x + y = 16 and -2x2 = -y+ 10.

Q: Find the area bounded by the curve y = - -x³x²+3x and the line y=x. 16 4 (A) 10 square units B 8…

A:

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

A: y=2x --------(1) y=x2+x-2 -------(2) For points of intersection…

Q: Find the area between the curves. x = 1, x = 2, y = 3x3 + 2, y = 0

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Q: Find the area of the region bounded by the curves y= 2² - 3 and y = 2x + 5.

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Q: Find the area bounded by the curve y = 4x over the square root of (1 - 2x) and lines y = 0, x = -4…

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Q: Calculate the area of the segment cut from the curve y = x(3 – x) by the line y = x.

A: here we have to find the area of the region bounded by the curve and line.

Q: Estimate the area under the curve y=64-x^3 between x=0 and x=4. Use four rectangles

A:

Q: Find the area of the region between the curves 4x + y^2 = 12 and x =y.

A: 4x+y2=12    and  x=y

Q: Find the area between the curves. 3x х%3 -2, х%34, у%33е3X, у%3D2е 3X +1

A:

Q: Find the area enclosed between the curve y = 9 - x squared and line y = x + 7

A: This question is based on application of integration.

Q: Find the area between the curves: y = x³ – 10x? + 16x - x³ + 10x² – 16x 3 and y = -x° + 10x?

A: Consider the figure given below :

Q: The area bounded by the parabola y = 4x2, y-axis and the lines y = 1, y = 4 is

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Q: Determine the area bounded by the curves x³ - y = 0 and y + 3x² - 4 = 0, using a vertical element.

A:

Q: Find the area between the curves. x = -2, x = 4, y = 3e3x, y = 2e3x + 1

A: The above question is from the application of the integration part and since the major part of…

Q: By double integration, Find the area between the line y=6-2x, the x-axis and y-axis.

A:

Q: . Find the area of the region bounded by the curves y = 2x? - 8x + 12 and y = -2x+ 12.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 2 y = 12 – 3x", y= 4 – x- — х |

A: Let's find.

Q: What is the area of ​​the region between the parabola y=x^2-1 and the line y+2x=2?

A: The solution is given below in the next step:

Q: find the area of the region bounded by the curves 4x - y2 = 0 and y = 2x - 4

A:

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: Find the area of the region bounded by the line y = 4 - 2x and the coordinate axes.

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

Q: Find the area between the curves. x = -5, x=2, y = 3x, y = x² - 4

A:

Q: Two curves having an equation of 2y² and y = 2x² x = intersect each other. Compute the area between…

A: A detailed solution is given below.

Q: Find the area between the curves.  y = |9x|  ,  y= x^2 - 10

A: First we graph the functions. They cut at (-10,90) and (10,90)Area from x=-10 to x=0 is equal to the…

Q: Find the area between the curves. y = x4/3, y = 2x1/3

A: y = x4/3, y = 2x1/3

Q: the

A: Given curve y^=x and y=√x  Line x-4=0   Find area ?

Q: area bounded by the curves y2= 6x and x2 = 6y?

A: Given curvesy2=6x or y=6xand6y=x2 or y=x26

Q: Find the area between the curves y = x2 - 8 and y = 4 - x.

A: Explanation of the answer is as follows

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: The area bounded by the curve y = 6x and the lines x = 7,x = 11 and x – axis ахis is

A: → y = mx is the equation of straight line passing through origin with slope m.→ Area of triangle =…

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

A:

Q: Find the area between the curves x=63-7y^2 and x=7y^2-63

A: Here two curves are given and we need to find the area between them. The curve equations are shown…

Q: find the area between the two curvesx=2-y^2x=y^4

A: Given thatx = 2-y2         ...(1)x = y4            ...(2)

Q: The area bounded by the curves: у-х, у-6-х аnd у-0.5х is:

A: see below the answer and explanation

Q: Find the area enclosed between the two curves y=4-x^2 and y=x^2-2x.

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Q: Calculate the area described by the equation y= -6x² +24x + 10, bounded by the lines x = 0 and x =…

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Q: Find the area enclosed between the line y 1 and the curve y = x2 – 4x + 4.

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Q: y=9-x2 and ミ-4

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Q: Find the area between the curves. y=x² - 23, y = 9 – 4x

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Q: Find the area of the region between the x-axis and the curve .3 y = x³- 4x - 2 < x<2 ?

A: Let us first plot the graph of y=x3-4x, -2≤x≤2.

Q: Find the area of the region bounded by the three curves y = x², y = 8 - x², and 4x - y + 12 = 0.

A: Given: y=x2y=8−x24x−y+12=0

Q: Estimate using right-hand endpoints, the area between the curves y=9x^2 +30 and y= 5-7x over the…

A: given :

Q: Find the area of the region in the first quadrant bounded by the line y=3​x, the line x=4​, the…

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Q: Find the area between the curves -16 = 4x- y and -10 = 2x-y.

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Q: y = 3x2, y = 0 and x 31

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Q: Find the area of the region between the curve y = √2x — 1 and the lines x = 1 and x = 5.

A: Given: The region between curve y=2x-1 and lines x=1 and x=5

Q: Find the area bounded by the curves, 2x² + 4x + y =0 and y = 2x.

A:

Q: = 4x y = 2x – 4

A:

Q: Find the area between the curves: y = x3 – 12x? + 20x and y = -a3 + 12x2 – 20x

A: Solution )

Q: Find the area of the region bounded by the line y = 2x – 5 and the parabola y = x² – 4x. - -

A: Graph of enclosed region -

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.