3. Find the area of the region bounded by the parabola y? = 2x – x and the line y = x – 5 by taking horizontal rectangular elements of area.

Q: Find the area of the region bounded by the parabola y² = 2x - 2 and the line y = x - 5. 16 17 18 19…

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Q: Find the area of the region bounded by the parabola y = x 2  ,the tangent line to this parabola at…

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Q: Find the area bounded by the curve ay = x² and the lines y = a and y = 4a.

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Q: area

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Q: 2 ア=x,y=2r

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Q: Find the area bounded by the parabola y=-x+3 and the line y=x+3. (i) Using vertical strips (ii)…

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Q: 1. Find the area of the region bounded by the parabola x = 3 + 2y – y? and the line 2x + 3y = 6.

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Q: Find the area of the region bounded by the parabola y² = 2x2 and the line y = x - 5. 16 17 18 19…

A: Given: y2=2x-2 and y=x-5 Now find the point of intersection between the given curves. y2=2x-2 ;…

Q: Find between the porabolas the area 2 2.y= X+2 メャ 2.

A: We first sketch the region using a graphing calculator

Q: 2. Find the area of the region enclosed by the parabola y = 2x² and the line y = -x-1

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Q: The area bounded by the curve x = 5y + 8, the y-axis and the abscissas y = 0 and %3D y = 2 is

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Q: The area of the region enclosed by the parabola y = 2 - x? and the line y = -x is :

A:

Q: 9. Find in two ways the area bounded by the parabola y = x², the y-axis, and the lines y = 1, y= 4.

A: Given,  The parabola y = x2  We have to find the area bounded by the parabola, y-axis and the lines…

Q: Consider the area formed by the curves f(x) = x² + 1, y = x°, and the y axis in the first quadrant

A: The area between the curves y=x3 and fx=x2+1 on interval 1.46557…, 2.46557…:   The area between…

Q: Find the area of the region bounded by the parabola y² = 2x − 2 and the line y = x − 5. 16 17 18 19…

A: y² = 2x -2  y = x -5  Here we have to find intersection point  x = (y² +2)/2  x = y+5  Compare both…

Q: The area of region bounded by the parabola y? = 4x and the line %3D y = 2x – 4 is -

A: We have to find the area of the region bounded by the parabola y2=4x and the line y=2x-4

Q: d) Find the volume of the solid formed when the area bounded by the curve y = 3x – x? and the lines…

A: The volume of the solid generated by the revolution of the area bounded by the curve y=f(x), x-axis…

Q: Find the area.

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Q: Compute the area contained between the parabolas y and y =4-

A: Given parabolasy=x23y=4-23x2

Q: Find the area of the region bounded by the curves y = y = -x² + 4x. 9/4 11/3 12/15 8/3 none of the…

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Q: The area bounded by the curve x = 4y + 7, the y-axis and the abscissas Y = 0 and y = 2 is 11 22 18…

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Q: (2) Determine the intersection points of y=-x² +9 and y = 5. Then find the area bounded by this…

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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

A: Given: Parabola: y2=x+3 and line : x-y=-1 To find : Area of the region bounded by the given parabola…

Q: Find the area between the graph of y = sin x and the line segment joining the points (0, 0) and ( 7/…

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Q: Find the area of the region R enclosed by the parabola y = x² and the line y = x +2. Solution:

A: " Since you have asked two questions, we will solve the first question for you, if you want second…

Q: Given the curve y = x´ and the lines y = 0 and y = 2 – x Find the area of the region bounded by the…

A: Given

Q: find the parabolas x= y2,y= 255¢ and the ine area Of the region bounded by the

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Q: Find the area enclosed by the given curves. y = x°, y = 4x 4. O 16 2 8.

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Q: B) Find the area of the region enclosed by the Parabola y = 2 – x2 and the line y + x = 0 ?

A: The region is bounded by y=2-x2 and y+x=0

Q: Find the area bounded by the given curves. v = 6x² – 16x – 7 and y = 3x2 + 2x – 22 | square units

A: Given curves are: y=6x2-16x-7y=3x2+2x-22

Q: Find in two ways the area bounded by the parabola y=x^2, the y-axis, and the lines y=1, y=4

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Q: s Show that the area of the plane region bounded by the curves, r-y = 7, r= 2y-y+3 is 9 sq. units.

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Q: Find the area lying between the parabola y = 4x – x² and the line y = x -

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Q: 17 - Calculate the area of the region between the y = x^2 – 3x parabola and the y = 3x line. O A) 36…

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Q: Find the area of the region lying between the r-axis and the curve In(3x) – 1 y = to the right of…

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Q: Find the area of the region bounded by the parabola x = 4y – y? and the line x = 2y – 3. %3D

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Q: Find the area of the region between the parabolas x=1 +yt and H=x-2x.

A: Area between curves.

Q: Find the area enclosed by the line y = x –1 and the parabola y = 2x + 6.

A: y2=2x+6 and y=x-1. To find: Area enclosed by the given two curves.

Q: Find the area of the region R enclosed by the parabola y-x and the line yー国

A:

Q: 3. Find the area enclosed by the two curves x = y² – 4y and r = 2y – y². |

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Q: The area of region bounded by the parabola y? = 4x and the line y = 2x – 4 is

A: In the given question, the concept of integration is used to find the area of the common region.…

Q: Find the area bounded by the parabolas (x – 2)² – 9py = 0 and y2 = 9p(x – 2). -

A: We need to find area bounded by two curves.

Q: 7) Find the area of the region enclusced by the curves y=x² and

A: Please refer the attached image for complete solution. THANK YOU !

Q: Find the area of the region enclosed by the line y = 2x + 4 and the parabola y = 4 - x2 in the…

A: The diagrammatic representation of the area is,

Q: Start with the area bounded by y=x^2 , y=0 and x=2, then rotate around the line y=4.

A:

Q: Given the curve y = x' and the line y = 2 – x. Find the area of the region bounded by the curve and…

A: Area bounded by the curve y=x2 and the line y=2-x

Q: Calculate the area of the region to the left of the parabola x= 2y^2, to the right of y-axis, and…

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Q: Find the area of the region bounded by the parabola y2 = 2x-2 and the line y = x-5 using (a)…

A: We will find out the required area.

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: Find the area of the region bounded by the parabolas x = y²,y = 2/x and the line y = x.

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.