Find the areas enclosed by the following curves: x = y2 – 1 and x = lyl/1- y2 X = x = y² – 1 1.0 0. - x = lyl /1- y2 -1.5 -10 -0.5 0- 0.5 1.0 -0.5 -1.0

Q: Find the area between the curves y = x²(x – 3) and y² + 8y – 16x + 48 = 0

A: Formula: The area between the curves on the interval given by, Given:

Q: Find the areas enclosed by the following curves: x = y2 – 1 and x = lyl/1- y² %3D

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Q: B- Find the area between the curves: x = y2 and y = x - 2

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Q: Find the area between the y-axis and the graph X = 543-2-1 1 2 3 4 5 (y - 3) dy = 6.500 (y - 3) dy =…

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Q: Find the area enclosed by the xx-axis and the curve x=t^3+1x=t3+1, y= 2t-t^2y=2t−t2.

A: Given curves are x=t3+1, y=2t-t2.

Q: Find the area between the curve x = 2r*, y = 31 +1 and the x-axis, 0<t<2 !!

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Q: Find the area enclosed by the curve x= t2-2t, y = √t and the y-axis.

A: The area enclosed by the curve x=t2-2t, y=t and the y-axis

Q: Sketch the region enclosed by the given curves. y = 17xl, y = x2 - 8 y 40 4아 20 20 ma x -20 -40 50…

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Q: Find the area between the curves y and y 3x + 2.

A: From y=x3, y=3x+2 solving for the points of intersections.…

Q: y = e²x and x - 2y + 5 = 0

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

Q: :) y = xva² – x²,a > 0 and y = 0 -

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Q: Find the area of the region enclosed by the line y=4 and the curves y=e^x and y=(x-1)^2

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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: Determine the area of the region between the following curve. x = |y| and 2x = −y^2 + 2

A: Given that, x = |y| and 2x = −y2 + 2

Q: Find the area between the curves. x = 0, x = 3, y = 2e3x, y = e3x + e6

A: To find the area between the curves, f(x)=2e3x and g(x)=e3x+e6, use the formula, A=∫ab[g(x)-f(x)]dx.…

Q: Calculate the area enclosed between the x-axis and the curve y = x2 - 1 between x = -2 and x = 2.

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

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 bound between the curves y = x² – 4 and y = x + 2 seen below.

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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: Find the areas enclosed by the following curves: y = xv1 – x2, and y = 0 | y = x/1 – x2 0.4 - 0.3-…

A: We have the given curve equation as y=x1-x2  and  y=0

Q: Find the total area of the region between the curve and the x-axis. y= 2x-x, 0sx s2 O A. 3 O B. 3.…

A: Explanation: Given that: y=2x-x2 Concept: The area under the curve  A=∫abfxdx here a=0b=2

Q: Calculate the area between the two curves y = ax³ and y 1.4 and b = 2.4. Give your answer to three…

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Q: Find the area enclosed by the curve  x = t 2 − 2 t , y = t  and the y-axis. Round to four decimal…

A: To Determine: find the area enclosed by the curve x=t2-2t  ,y=t and the y-axis.Round to four decimal…

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 inside the curve x =1– t², y =t-t (-1<t<1).

A: Given, The curve  x = 1-t2   and  y = t -t3 -1≤t≤1   We have to find the area inside the curves.

Q: Find the area between the curve inclosed by the curve x = 2y^2 and the curve x = 4 + y^2

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Q: Find the area enclosed by the y-axis and the curve x = t - t2, y = 1 + e-t .

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

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Q: Find the total area of the shaded region bounded by the following curves. x= 6y? - 6y x= 4y - 4y x=…

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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 between the curves y = e 1. = y = 2.3x + 1 from x = 0 to x = Area -0.4x and

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Q: Find the area between the curves. x= 0, x= 3, y=2 eX, y= e³ 3x + e

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Q: Find the area enclosed between the x-axis and the curve y = (x+ 3)²,0 < x < 1.

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Q: Find the area enclosed by the curve ax =y(2a– y).

A: This question is based on application of integration.

Q: Find the area enclosed by the curve x = t2 - 2t, y = Vt and the y-axis.

A:

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: Find the area of the region enclosed by the given curves  y = 1/4x^2 y = 2x  x+y = 3 while x is…

A: I have done solution step by step in detail...go through the solution

Q: 4. Find the area enclosed by the curve: x=t2 – 2t, y= vt and the y-axis

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Q: The curve y = √x + 2 is revolved about the y-axis from x = 1 to x = 8, find the surfac area.

A: Here we have to find the surface area.

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: Determine the exact area enclosed between the two curves y = (x)^1/2 and     y = 1/2(x)

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Q: Find the areas enclosed by the following curves: (d) x = y² – 1 and x = lyl/1- y2

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Q: Find the area between the curves y = e0.3se y = 1.9x + 1 from x = 0 to x and = 5. Area =

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Q: Find the area between the curves y = x² and y = x'. 1.6 1.4 1.2 11 0.8 0.6 y =x? y = x3 0.4 0.2 0.2…

A: Solution: The curves intersect at the point (0,0) and (1,1). y = x2 and y = x3

Q: Find the area of the region in the first quadrant bounded by the curve y = √x² + 5, the x-axis and…

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Q: (iii) x=-y² +10 x = (y- 2) -1 -가

A:

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

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.