Find the area bounded by the given curves.y = x2 − 3 and y = 12 − 14x2                                                  square units

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 bounded by the curves: 3x y = x² + y = 5, and x = 0. %3D x2 + 2 This area is in the…

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Q: i. Find the exact area between f(x) 7x + 10, the x-axis, x 0, and x = 5.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the area under the region below y = e® and above the x-axis for 0 < x < 2.

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Q: Find the area bounded by the parabola x = y² + 2 and the line y = x – 8. 11 -2 3.

A: We have to find out the area bounded by the two curves

Q: Find the area bounded by y = x? and y = 6x – x². A. 9 В. 27 С.6 D. 18

A: the given figure is: we have to find the area bounded by y=x2 and y=6x-x2.

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: 1. Find the area of the region enclosed by the equations below. y = x² – 2x and y = x

A: Given function :

Q: Find the area between the graph of y and the r-axis for a E [0, b] where b is a (2x2 + 1)2 positive…

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Q: Find the area between the x-axis and the curve y = -x² - 2x, -3 ≤x≤ 2.

A: Solution: Given that Curve is y = -x^2 -2x Area between the x axis and the given curve is

Q: Find the exact area enclosed by the curves, y=x5 - 6x3 + 4x and y = x.

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Q: Find the area bounded by the parabola x² = - (y - 1) and the first quadrant.

A: Intersection points:y=0x2=1;x=1 (First quadrant)(1, 0)x=0:1-y=0y=1(0, 1)

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

A: Given: The line is y = x-1 and the parabola is y2=2x+6   To determine: The area enclosed by the line…

Q: Find the area enclosed by the parabola y=4x-x^2 and the x-axis.

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Q: 3. Find the area between the curves x2 2ay and x? = 4ay – a².

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Q: Find the area between y = x^2 + 4, x = 1 and y = 0.

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Q: Find the area between x = y^2 - 4, y = e^x

A: To find - area

Q: Q2. Find the area enclosed by the curve y = x³ – 3x² + 2x and the x-axis.

A: To find the area enclosed byy=x3-3x2+2x and x-axis

Q: Find the area between the graph of y = and the x-axis for x e [0, b] where b is a (2x2 + 1)2…

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Q: Find the area bounded by y = (11 – x)7, the lines 3x=2, x=10, and the x-axis

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

Q: y = e2x, y = e*, and x = 2

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Q: Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

A: We have to find the area between the curve y=x3-6x2+8x and the x-axis.

Q: Find the area bounded by the curve a?y = x3 the x- axis, and the line x-2a. Solve with respect to x.…

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Q: Find the area bounded by the line x-2y + 10 = 0, the x-axis, the y-axis and x=10.

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Q: The area bounded by the curve y = 6x , the x-axis and the ordinates x = = 0, x = 2 is 6 O 3 O 12 O…

A: area bounded by curve and x axis given by integrating curve

Q: 4. Y = x2 (x-3) and y?+ 8y -16x + 48 = 0

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Q: Find the area enclosed by the line y = x – 1 and the parabola y? = 2x + 6. %3D

A: To find the area enclosed by the line y = x - 1 and the given parabola.

Q: Q2. Find the area enclosed by the function e and the x-axis.

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Q: The area formed by the boundaries y=1, x=2, and y=e^(-x) is closest to:

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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: 2. Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

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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 area enclosed by the given curves. y = 2x-x2,y 2x-4 31

A: Explanation of the answer is as follows

Q: Find the area within the curves y = 25 – x², 256x = 3y², and 16y = 9x %3D %3D

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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…

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Q: Find the area bounded by the parabola x² = 4y and y = 4 A. 21.33

A: Solution of the problem as follows

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: Find the area enclosed by the line x=y and the parabola 4x+y² =12

A: Given:         The line x = y  and the parabola 4x + y2 = 12   To find:           The area…

Q: Find the area bounded by the given curves: (answers in square unit) a)y = x2 − 5 and y = 4 − 8x2…

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Q: 1. Find the area enclosed between the graphs of y = 5 – 10x + 7x? – a3 and y = 4x – 3.

A: given equations are

Q: Q2. Find the area enclosed by the function e* and the x-axis .

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Q: Find the area bounded by the parabola y2= 4x, the x – axis and the lines x=1 and x=3.

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

A: The red line is x=10 and the blue line is given line i.e. x-2y+10-0 Given x-2y+10=0This can be…

Q: Find the area bounded by the curve y=x^2, the axis, and the ordinates are x=1 and x=3.

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Q: Solve the area bounded by y3 + 10y + 5 = x², the y-axis and the lines y=O and y=3

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Q: Find the area in square units bounded 1) y2 = 4x, x=0 to x= 4

A: Area Bounded by the curves :   If x=f(y) and x= g(y) be two continuous function on a,b and f(y)…

Q: 19. Find the area in the first quadrant bounded by the parabola y² = 4x and the line x = 3 and x =…

A: The equation of the curves are C1: y2 = 4x ⇒ y =2xC2: x= 1C3: x = 3 To evaluate: The area of the…

Q: 6 Find the area enclosed by the given curves. * y = x³ and y = 4x

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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.