1. (a.) Find the area bounded by the two curves; y=r+x-10 and y=-+Sx+6. i y=r-3r and y = 2-x

Q: find the area bounded by the curve y = (1 + x^2) / (2x^2) and the lines y = 0, x = y, and x = 2

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Q: Find the area between (bounded) by the Curves y=x² +10x and y= 2x + 9°

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Q: 2. Find the cerntroid of the area bounded by the curve y= 2x + 1 x+y =7 and x= 8

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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: 2. Find the area bounded by the curves y = x² and y = 2 – x².

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Q: Find the area bounded by the following: 1. Curve y²-8y-8x +32= 0 and y²-8y + 4x = 0

A: We will use basic knowledge of integral calculus and the theory of evaluation of integrals.

Q: Find the area bounded by the given curves. 1. x^2=4y , 3x-4y+4=0

A: The area between the curves is the area between a curve fx and a curve gx on an interval a,b given…

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: 15 Find the exact area enclosed between the curve y = v4 – x and the line r-y+2 0.

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Q: y = e²x and x - 2y + 5 = 0

A: x-2y+5=02y=x+5y=x+52The equations are: y=x+52y=e2x

Q: Find the area bounded by the given curve: 16x² +9y² − 64x + 18y-71 = 0 and x² + y² − 4x − 4y+4=0

A: Given the curves, C1:16x2+9y2-64x+18y-71=0C2:x2+y2-4x-4y+4=0. Rewriting, we get…

Q: 6. Find the area bounded by the curve ay = x² and the lines y = a and y = 4a.

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Q: (b) Compute the total area between the curve and the x-axis over the interval [-1,9]. y = f(t) 10…

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Q: y = e²x and x - 2y + 5 = 0

A: I am attaching image so that you understand each and every step.

Q: The area bounded by the curve x = 3y + 8, the y- axis and the abscissas y = 0 and y = 2 is O 19 O 1…

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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: 5. Calculate the area contained between the curve y = cos x, -T < x < T, and the line

A: To calculate the area contained between the curve y=cos x, -π&lt;x&lt;π, and the line y=12. Note: As…

Q: - 7. Find the area bounded by the curve y² + x − 4y = 5 and the y — axis

A: We have to find the area of the given curve and line.

Q: 1. Find the area bounded between the curves: y = x°, x = 1, and y -8

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Q: 1. Find the area bounded by the curves y – 2 = x² ,y = 6 and the y – axis ( in Quadrant I only), as…

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Q: Compute the area between the following curves y = x° and y = -3x2 on the interval |0, 2|

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Q: 2. Find the area bounded by the curves y = x² and y = 2– x².

A: To find the area bounded by curves

Q: Enclosed by x² + 4y² = 16

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

Q: Find the area bounded by the curve x2 + y2+4x-14y +44 0

A: Topic:- area of circle  Note:- as per our guideline if more than one question uploaded than only…

Q: Find the area bounded by the curves y = 6 – x² and y = 8 – 3x. 1 a) 6 1 b) -/6

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Q: Find the area bounded by the two curves f(x) = x² – 8x + 8 and g(x) = - 2² + 6x – 8, and the two…

A: To find Area between two curves:  f(x)=x2-8x+8 and g(x)=-x2+6x-8 and two vertical lines x=3 and x=4.…

Q: Find the area between the curves x=y² –1 and x = 2y² – 2.

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Q: 1)Find the area bounded by the given curves. a)y = 3x2 − 12 and y = 0 b)y = x2 − 2 and y = 10 −…

A: we have been given the function y=3x2-12 and y=0 and the formula of the area under the curve is…

Q: Find the area bounded by the curves y = 6 – x² and y = 8 – 3x. 1 а) 1 b) c) d) 12 e) 12 -/3

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Q: Find the area bounded by the given curves. y = 2x - x2, y = 2x- 4 32 O A. w/ 3 37 OB. 3 31 OC. 3

A: The objective is to find the area bounded by the given curves

Q: 10. Find the area bounded by the curve x = y² + 2y and the line x = 3.

A: Area Bounded by the Curves : If f(y) and g(y) are two continuous function on a,b and f(y)≥g(y), then…

Q: ind the area bounded by the curve y²=4x, the lines x=1 and x=4.

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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: b) Find the area bounded by the curve: y = 8x – x² and y = 3x %3D %3D

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: problem in photo attached

A: Consider the given functions:

Q: Find the area between the curves defined by f(y) = y²+ 1, g(v) = 0, y = -1, y = 2

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Q: Find the area between the curves y = x² + 5x and y = 3– x² between a = -2 %3D and z = 0.

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Q: 1)Find the area bounded by the given curves: a)y = 6x2 and y = 24   b)y = 3x2 − 12 and y = 0

A: The given function are y=6x2 and y=24. The area bounded by the given curves as shown below:

Q: x = y² - 2y and x = 4y - y²

A: The given curves are; x=y2-2y and x=4y-y2 Now find the point of intersection between the given…

Q: 7. Find the area bounded by x = t2,y = 1– t3,0st<1 and the y-axis

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Q: Find the area of the region bounded by the given curves: yx = 1, y= 0 , x = 1, x= 3

A: Given: Find the area of the region bounded by the given curves: `yx=1 y=0 x=1 x=3`

Q: Find the amount of bounded area between y = sin x and the line y = -1+-x from x = 0 to x = T.

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Q: Find the area under the curve y 2 I over the interval [1, 4]

A: Find the area under the curve y=2x over the interval [1, 4]

Q: 4. Find the area bounded by the given curves:y² = x + 4, x - 2y + 1 = 0

A: Answer is given in next step.

Q: Q1: Find the area bounded by: The curve y=4x-x and the lines y=0, x=1 and x=3.

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Q: What is the area bounded by the curve x^2=-9y and the line y+1=0. O 3 O 4 O 5

A: Given equations: x2=-9yy+1=0

Q: Find the area between (bounded) by the curves y = x2 + 10x and y = 2x + 9.

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Q: 17) Find the area bounded by the curve 4x - 3y + 19 =0, y-axis, the lines y = 1 and y = 5.* O a) 15…

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Q: Find the area bounded by the curve y=x^2 and the line y-4=0. O A. 16/3 В. 32/3 О с.0

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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.