Compute the area bounded by the curve y = 3x - x2, the x-axis and the ordinates x = 2; x = 4.

Q: Find the area bounded by the curves y2 = 4x 4х + у — 6 %3 0

A: We need to find the area bounded by the curves y2=4x4x+y-6=0

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

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Q: 3. Find the area bounded by the curves x2 + y2 = 9 and 4x2 + 9y² 36, on the first quadrant.

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

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Q: . Find the area bounded by the given curves. y = 9x² and the x - axis.

A: First we find point of intersection of curve y=9-x2 and x-axis. Put y=0, 0=9-x2 x2 =9 x=±3 Therefore…

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: 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 curve y^2+x-4y=5 and the y-axis

A: Given: curve is y2+x-4y=5

Q: Find the Area bounded by the given curves. y = 2x + 1 ,  y = 7 - x ,  x = 8

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Q: Find the area bounded by y²=4x and y+2x=12.

A: To determine the area of the region bounded by the curve : Draw the given curves. Observe the…

Q: Find the area bounded by y = x² + 6x and the x-axis from x = -1 to x = 4.

A: Find the area

Q: Find the area bounded by the graphs of y = 3x2; x = 0; x = 2; and the x axis.

A: Given,

Q: Find the area bounded by the curve y= lnx, the x– axis, the line x = e². A =1+e?

A: Use area formula

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

A: We have to compute the area of the region bounded by the curve y=13x3-3x and the line y=-4 using the…

Q: Find the area bounded by the ff. curve and line: y = xe^– x , the x-axis and the maximum ordinate

A: The curve y=xe-x, we have to find the area bounded by the curve, the x-axis and the maximum…

Q: Find the area bounded by the indicated curves. y=x",y 2-x, x = 0 (x20)

A: Given the curvesy = x2 (red line) ,  y = 2-x (blue line) and x = 0 [green line] (x≥0 )Check the…

Q: Find the area bounded by the curve y = x² and the x-axis and the ordinates x = 1 and x = 3

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Q: Find the area bounded by the line f(x)=2x+2, the curve G(x)=X^2-6X +9 and the two vertical lines X=1…

A: Given:       fx=2x+2        gx=x2-6x+9        x=1,x=5 Area bounded by line and curve is:…

Q: Find the area bounded by the curve x=y²+2y and the line x=8.

A:

Q: Find the area under the curve over the indicated interval. 5. y = x - x2; (0, 1] 6. у 3 [1, 3]

A: y = x-x2 ; [0, 1] y = 4/x; [1, 3]

Q: Find the area bounded by the curve y = 3x²/4 and the lin 3x – 2y + 12 = 0.

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Q: Find the area bounded by the curves y = 3e2x and y = 3e-x and the ordinates at x = 1 and x = = 2.

A: The region is

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

A: Given: y=x2, x=1, x=3, and x-axis or y=0. So, from the given curves the bounded region is as shown…

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: Enclosed by x² + 4y² = 16

A: We have to find area bounded by given curves.

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

A:

Q: Find the area bounded by the curve y = Vxe¬v* and the x-axis from x = 0 to x = 4.

A: We want to determine the area bounded by the curve y=Vxe-Vx and the x axis from x=0 to x=4 with…

Q: Find the area bounded by the curve y = 7x In(x), the x-axis, and the lines x = 1 and x = e.

A: Given:y=7xlnxlines x=1 and x=eTo find:Area A=??

Q: Find the area in the second quadrant bounded by the curve y = x' +4x² – x – 4 and the x – axis.

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Q: y = 9x²; x-axis

A:

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 y2 = 4x and y = 2x – 4.

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Q: Find the area enclosed between the x-axis and the curve y = (x+ 3)²,0 < x < 1.

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Q: Compute the area bounded by the curve y = x² – 2x , the x-axis and the ordinates x = 1; = 3.

A: We have to find the area bounded by curves

Q: find the area bounded by the curve y=9-x^2 and the x-axis

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Q: Find the area bounded by y=2x-x^2 , the x – axis, and the lines x =0 and x= 4.

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Q: . Find the area bounded by y = (11 – x), the lines 3x=2, x=10, and the x-axis.

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Q: Find the area bounded by y = x^4 and the x-axis from x = -2 to x = 2

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Q: 7. Find the area bounded by the curve y = x e¯** , the x-axis and the maximum ordinate.

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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 given curves. x2 = y - 1 and x = y - 3

A: From the given curve   x2=y-1 ; x=y-3   Now finding the point of intersection for both curves:…

Q: Find the area bounded by the curves y=(x^3)-18x and x+2y=0

A:

Q: Find the area under the given curve over the indicated interval. y =x*; (1, 3]

A: The area under the given curve = 48.4

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

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Q: Find the area bounded by the curves y - x² = -3,x+y = 3 and y = 0.5x.

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Q: Find the area bounded by the curves y=ex+2, y-axis, y=1, and the line x=3

A: Find the area bounded by the curves y=ex+2 and y-axis, i.e., x=0, y=1, and the line x=3. Limit for x…

Q: Find the area bounded by the curve x^2=4y+4 and the line y=x+2

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Q: Compute the area bounded by the curve y = x2 + 3, the x-axis and the ordinates x = 1; = 4.

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Q: . Calculate the area bounded by the curve y= 4(x – 1) and the x -axis. A)

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Q: Find the area bounded by the curve y=10+4x+x^2 and x-axis from x=-3 to x=-1.

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.