The area of the region bounded by the curves x = y2 +1 and y = x -3 is 2 -1 16 (A) 17 (C) 3 (D) 4 13 (E) (F) 9 C Windows bui Windows buiiil slacl wI Jäil O A O O O O 000

Q: The area of the region bounded by the two curves y = x²and y 25 is Square Units

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Q: Find the area of the region bounded by the curve y = xe and the raxis from x- 0 to x =3 0.5 -0.5

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Q: Sketch the region bounded by the graphs of the equations f(y) = y2 + 1,        g( y) = 0, y = −1, y…

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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: The lower, upper limit in the evaluation of the area of the region bounded by the two curves y = x…

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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 two curves y=x²-4 and y = x - 4 is given by

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Q: a) Find the area of the region enclosed by the curve y=x²-2 and by the line y = 2. y=x²-2 y=2 Co

A: Area of a closed region is given by  A=∬dydx, when the strip of area is parallel to y-axis.

Q: y2 = 4 – x and y² + y = x + 2

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Q: y = In(x +6) y = 3lnx x = 0 y = 0 Calculate the area of the region bounded by the curves

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Q: Evaluate xydxdy over the region bounded by x axis, ordinate x = 2 and the curvex² = 4y %3D OA 3 О В.…

A: The shaded region shown in the figure is the area of integration

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

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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: To find the area of the region bounded by the below curves. y=9−x2y=xy=0 x−axis

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

A: Given that:                      y=x2+9y=10+2xBetween [-1, 3]   NOTE: As per our answering…

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

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Q: Find the area of the region between the line y=2x and the curve %3D y =x² +x-2.

A: Given:          y=2x and the curve y=x2+x−2

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

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Q: The area of the region bounded by the curves y = 3x – x² and y = 2x is 5 а. 3 O b. 32 3 С. d. 1 6.…

A: We need to find the area of region bounded by the given curves. For that, we need to find their…

Q: V2y + 6 5. Find the area of region bounded by the curves and *-y-1.

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Q: Let R be the region bounded by the parabola y = x − x2 and the x-axis. Find the equation of the line…

A: Given information:

Q: Given that R is the region bounded by the curve y = x+3 and line y= x-3. (b) Describe the region Rby…

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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: 1/ Find the area of the region enclosed between the curves y= 2r²+10 and y=4x+16 and ,x=-2 and x-5?…

A: Given          y=2x2+10    and  y= 4x+16,   x=-2 and   x=5.

Q: /2y +6 5. Find the area of region bounded by the curves and *- y-1

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Q: 2. Find the area of the region enclosed by the curve =x- 4 and y = x - 2.

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Q: The area of the region between the curve y x'-6x+ 8 and the x-axis & x=0; x= 3 is given by -6x+8)kke…

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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.

A: The given curve is y2=4x and lines x=2 and x=4. From the given information,

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 D is the area in the XY-plane bounded by the X-axis, Y-axis, and the 4x + line 5y = 0.…

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Q: 1. Find the area of the region bounded by the curves y = 3x and y=x².

A: Given : The curves y=3x and y=x2. The objective is to find the area of the region bounded by the…

Q: 3/Find the area of the region ecloseed by the curves y=cost and y=0 on the intervalL A-2

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Q: Find the area of region bounded by the curves x= 2y+6 and x y-1.

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Q: Find the area bounded by the curve x=16-v² and the curve x=y-5y+4 as shown in figure below. x = y² –…

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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: While evaluating the area of the region bounded by two curves Vỹ = x and y - 11z + 24 = 0, the…

A: Given: Two curves y=x and y-11x+24=0 are intersecting each other. The objective is to find the…

Q: 1/ Find the area of the region enclosed between the curves y= 2x+10 and y=4x+16 and ,x=-2 and x=-5?…

A: Area under curve

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 curves y² - 4x = 5 and 4x + 3y = −1

A: We can find the area of the region between the two curves using the double integration method. We…

Q: R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

A: Given regions are, y=x2y=4x-x2y=0 Now, using Washer method by the formula, V=π∫abR2-r2dx

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 propeller-shaped region enclosed by the curves x - y1/3 = 0 and x - y1/5 = 0.

A: We have the curves x-y13=0 and x-y15=0. We have to find the area of the propeller-shaped region…

Q: 3. Find the area of the plane region bounded above by y = 1 -|x-1| and below by the x-axis. y = 1…

A: Here we have to find the area bounded by the given regions.

Q: The lower, upper limit in the evaluation of the area of the region bounded by the two curves y = and…

A: Given curves are: y=x2 ............(1)y=10x-16   .........(2)

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 absolute maximum and minimum of the function f(x, y) = x²y - ry³ on the region bounded by…

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

A: The region bounded by the curves are y=x3-8x2+20x , y=-x2+8x…

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.