The area bounded by the curve y 4x and the lines r = 6 ,x = 10 and a axis is

Q: Find the area of the region in the first quadrant bounded by the line y=2​x x=4​ y=2/x and the​…

A: The given region is bounded in first quadrant by following curve: y=2xx=4y=2x and the x-axis.…

Q: Find the area bounded by the curve y = x exp(-x²), the x-axis and the vertical line passing through…

A: Given: The given curve is, The x-axis and the vertical line passing through the maximum coordinate.…

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

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Q: Find the area bounded by the parabola y2 − 3x + 3 = 0 and the line x = 4. With illustrations please

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Q: Find the area bounded by the curve y = x2, AB is tangent to this curve at point P (2,4) and the x-…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: What is the area (in square units) bounded by the curve y' =x and the line x- 4=0?

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Q: x = y² and the line y = x − 2

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Q: Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

A: We have to find the area .

Q: Find the area bounded by the curve x^2 + 4y - 8 = 0, the x - axis, and the lines x = 3 and = 5

A:

Q: What is the area bounded by the curve x^2 = -9y and the line y + 1 = 0?

A: Solution:Givenx2=-9yy+1=0To find the area bounded by the curveFormula:Area=∫abf(x)-g(x)dx

Q: Find the area bounded by the curve x y2 +2y and the line z = 3. %3D

A: Given :                curve x = y2 + 2y and the line is x = 3 To find :               The area…

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

A:

Q: Find the area of the curve bounded by the curves y=x* and y=3x+4.

A: We have to find th: e area of the curve bounded by the curves y=x4 and y=3x2+4.…

Q: Find the area bounded by the curve y = x2, AB is tangent to this curve at point P (2,4) and the x-…

A:

Q: What is the area bounded by the curve x² = -9y and the line y + 1 = 0?

A: Given curve is x2=-9y Line is y+1=0 We need to find the area bounded by the curve

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: Find the area in the first quadrant bounded by the curve y = 3x – x, the lines x = y = 2. 0 and

A: To find the area of the region bounded by the curve we use the formula Area=∫abf(x)-g(x)…

Q: Find the area between the curves. x = -2, x = 1, y = 2x, y = x2 - 3

A: Given curves,  y = 2x y = x2 - 3 x = -2 x = 1 To find the area enclosed.

Q: Find the area in the first quadrant bounded by the cubic 3x - x^3 and the lines x = 0 and y = 2.

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Q: What is the area of the region enclosed by the curves y=e^x, y=x^2-1 and the lines x=-1 and x=1?

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

A: Sketch the region and integrate in y variable.

Q: FIND THE AREA BOUNDED BY THE PARABOLA x = 8+2y-y², THE Y-AXIS, AND THE LINES y = -) AND y = 3

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Q: The area bounded by the curve z = y.y-axis and the lines Y3D0. y32 is s

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

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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: What is the area of the region enclosed by the curve y=x^2 and the lines y=x+6, x=0 and x=5?

A:

Q: The area of the region bounded by the curve y= e", the x-axis,'the y-axis, and the line x 2 is equal…

A: We have to find the area of the region bounded by the curve y=e2x , the x-axis, y-axis and the line…

Q: Find the area bounded by the curve y = 3x – x3 and the line y = 2

A: Given: y= 3x-x3; y=2 If f(x)> g(x) in the interval x=a to x=b, then the area between two curves…

Q: What is the area bounded by the curve y = x3 and x = -2 and x = 1? What is the area bounded by the…

A: we have to find area

Q: 2. Find the area in the first quadrant bounded by the curve y = 3x – x³, the lines x = 0 and y = 2.

A: Given- y=3x-x3 To Find- The area in the first quadrant bounded by the above curve, the lines x=0 and…

Q: Find the area bounded by the curve 16 square units 10 square units 8 square units 4 square units 16…

A: The region is bounded by y=116x3-34x2+3x and the line y=x.

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: What is the area bounded by the curve y^2 = x and the line x - 4 = 0?

A: We have to determine area of bounded

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

A: y = x4/3, y = 2x1/3

Q: find the area of the region bounded by the curve y^2=x+1 , both by the x and y axes and the line x=8

A: Using Reimann sums, the area of the region R is given by Sn=∑k=1n∆Ak. This is simply the sum of…

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

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Q: Find the area on the first quadrant bounded by the curve y = 2Vx and the lines y = 1,x = 4 and the…

A:

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

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

Q: What is the area bounded by the curve y = x3, the x-axis, and lines x= - 2 and x = 1?

A:

Q: Find the equation of a horizontal line that equally cuts the area bounded by the curves 2y=x^2 and…

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Q: Find the area between the curves x=y^2/2 and y=x-4

A: First we draw the curves using graphing calculator.

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

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

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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 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 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

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.