%3D %3D 3. The area bounded by y = -÷(x-1)2 + 4 , and the lines x =1, y = 2, and y = 4 rotated about the y-axis.

Q: Find the area of the shaded region. y = JX - 3 (16,1) 16 (0,-3) Select one: A. 22 В. 38 3 O C. 16 D.…

A: Area of shaded region can be find as follows

Q: Find the area: y = sin x, the x-axis, the y-axis and the vertical line x = 2 *

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Q: Find the area of the shaded region below. yA x=y² - 2 y 1 x=e y=-1

A: Given: Eq1 : x = ey  Eq2 : x = y2 - 2  Limit y = -1 to y = 1

Q: Find the area enclosed by the curve x² + 8y + 16 =0, the x axis, they axis and the line x-4 = 0. A.…

A:

Q: Find the area of the shaded region. y 2+ y = x+ – 2x3 1 y = 0 2 -1 i

A: Given, The function  ; y = 0   and  y = x4 - 2x3  the limits : x = 0  and x = 2 We have to find the…

Q: Find the area enclosed by the given curves. y 2x-x, y-2x-4 37 34 OB. 3. 31 32 3 D.

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Q: Find the area bounded by the curves: y=-3x/(x2+2) , x2+y2=5, and x=0. This area is in the fourth…

A: The solution are next step

Q: Find the area enclosed by the line x = y and the parabola 4x+y^2=12

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Q: Sketch the region enclosed by y = e, y = e¹0, and x = 1. Find the area of the region.

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Q: Find the area enclosed by the x-axis and the curve y=9- x². 32 square units 3 A B 36 square units 32…

A:

Q: Find the area of the shaded region below. yA x = y² - 2 y 1 x=e' y =-1

A:

Q: b) Find the area of the shaded region. 1) ii) y= T x=-y 2Fx= 2- y²

A: we have to find the area of the shaded region.

Q: 23. (x – 1) dA; R is the region in the first quadrant enclosed R

A: Given: ∬R(x−1)dA=?

Q: Find the area of the shaded region, if it exists. (If an answer does not exist, enter DNE.) y -6 x…

A:

Q: Find the area enclosed by the x-axis and the curve y=4-x2. A 18 square units 32 B square units 3 ©…

A: topic - area under the curve

Q: Find the areas below. b) The area bounded by the parabolas y = 6x - x² and y = x² – 2x. (Round…

A:

Q: 7. Find the area enclosed by the x-axis and the curve y = -x² + 9. 32 s.u. а. b. 18 s.u. с. 36 s.u.…

A: Area enclosed by the curve y=-x2+9.

Q: The rectangle shown below has one side on the positive y-axis, one side on the positive x-axis, and…

A: A rectangle has one side on the positive y-axis and one side on the positive x-axis. The upper…

Q: B: Find the area of the shaded region show y y =1+x X=-1- y=-1 Fig(1)

A: According to the given below figure:  area of the shaded region is…

Q: Find the area of the shaded region. 44) 2) (II/4, 2) TE: II II 2 311 4 y = 2 y = csc²x X

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: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the area enclosed by the x-axis and the curve y = -x² + 9. ... 32 А.) В.) 18 s.u. s.u. C.) 36…

A: Topic = Area Area = 36 s.u.

Q: Find the area enclosed by the x-axis and the curve y = -x² + 9. 32 A.) s.u. B.) 18 s.u. C.) 36 s.u.…

A: Follow the procedure given below.

Q: Find the area enclosed by the x-axis and the curve y = -x2 + 9. A.) * 32 s.u. В.) 18 s.u. C.) 36…

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Q: Sketch the figures and show step by step solutions. Find the area between the curve y = x3 – 6x2 +…

A:

Q: Find the area of the shaded region below. yA x= y² – 4y (-3, 3) x = 2y – y² X :

A: The region is bounded by the graphs x=2y-y2 and x=y2-4y

Q: 10 -1.2 dx

A:

Q: 25. yA y = y = V1 – x

A: We have to find the area of the shaded region of the image.

Q: Find the area of the shaded region below. yA x= y² – 2 y = 1 x= e y =-1

A: We calculate area by using double integral as following:-

Q: y=x² +2x+1 and y = 3x +3 The area of the plane region is?

A: "Since you have asked multiple questions, according to our guidelines we will solve only the first…

Q: Find the area enclosed by the curve x² + 8y + 16 = 0, the x-axis, the y-axis and the line x = 4. А.…

A: From the given curve the bounded region shown below:     Given curve:   x2+8y+16=0⇒y=-x2-168x=0 ;…

Q: Find the area of the shaded region. y x= 2 y = 2 e* y= 5 x– 1

A:

Q: Find the area bounded by the line x – 2y + 10 = 0, the x-axis, the y-axis and x = 10. A. 75 В. 100…

A: SOLUTION-

Q: Find the total area between the curve y = x³ and the X-axis between x = -2 and x = 2. y = x3 а) b) 8…

A:

Q: c) Find the area between: y = 2x + 3 and y = -x² + 10x – 9 %3D

A: We first sketch the region using a graphing calculator The functions intersect at x=2 and x=6

Q: a) Find the area of the curve x²/3 +y2/3 = a²/3 %3D

A:

Q: Find the area in the first quadrant, bounded by the lines x = 2a, y = 4a, the axes and the curve…

A: Given: x=2a, y=4a    and  the curve x2y=a3

Q: Find the area of the shaded region. 1) y = X - 3 (16,1) 16 (0,-3) 29 A) - 38 16 B) D)- 3

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Q: Find the area of the shaded region below. y x = y² – 2 y=1 x=e> y=-1 Area =

A:

Q: Find the area of the region included between the parabolas y? = 4(p + 1)(x +p+ 1), and y? = 4(p² +…

A: Here we have to find the area of the region bounded by the two parabolas.

Q: Find the area within the curves y = 25 – x², 256x = 3y², and 16y = 9x². C. 36.27 units² D. 32.67…

A: In this question we have to find area within the curves

Q: Find the area enclosed by the x-axis and the curve y= 9 – x². (A) 36 square units B 18 square units…

A:

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

A:

Q: Sketch the region enclosed by y = e3, y = e0*, and a = 1. Find the area of the region.

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Q: Find the area of the region between the line y = x — 4 and the parabola y2 = 2x

A:

Q: Find the area of the shaded region below. y 4 x= y² -2 y = 1 x= e" y=-1

A: Given

Q: Find the area of the shaded region. 12) y = Jx - 3 (16,1) 16 (0, -3)

A:

Q: The area of the shaded region: y-24 -1 (1.2) 2 3 5n

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Q: Find the area of the shaded region. y = e" 4 -1 1 (e - 1)/4 4e 1/4 e/4

A:

Q: y1=x2+2x+1 y2 =2x+5 Find the area of shaded region

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.