Find the area bounded by the given curves. y = 3x2 and y = 27

Q: a) Find the area of the region enclosed by the curves y = 12 – x² and y = x2 - 6. Answer: A =

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Q: Find the area bounded by the indicated curves. y=6-6x, y=D0 The area is square units.

A: The given curves:y=6-6x2, y=0We need to find the area bounded by the given curves.

Q: Find the area of the shaded region. 10 e e 3 y 3- x = y - 4 y = 1 X = -2 4 y = -1 3.

A: The shaded region is the area between the curves x=y2-4 and x=ey where -1≤y≤1. That is,…

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

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Q: termine the area that is bounded by the graphs of the following equations. y = 36x, y = x3

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Q: Find area of the region under the curve - 2 y = and above the x-axis, for 9 < r<11. area =

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Q: Q3) Find the area of the region enclosed by the curves: y y = x, and y = 1

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

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Q: Find the area of the region enclosed by the parabola x² and the x-axis. Y = 10x AREA :

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Q: Find the area bounded by the curve y = 8 – x and both coordinate axes in the first quadrant. Area of…

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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: Find the area between the corves y= 2-x² and

A: Find the area between the two given curves First draw both the equations in a single plane To draw…

Q: Find area bounded by the circle x? + y² = 25, the y-axis and the parabola y = 6x – x².

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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 enclosed by y = 2x and y = x.

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Q: Find the area of the region(s) enclosed by the curve y= |2x-6|, the x-axis, and the lines x =0 and x…

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Q: Find the area of the region bounded by the curves, x = -6, x = 6, the x- axis and the parabola x? -…

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Q: Sketch the region enclosed by y=e^4x,  y=e^8x and x=1. Find the area of the region.

A: Given curves are  y=e4x, y=e8x and x=1. The graph is

Q: B\\ Find the area of the region enclosed by the parabola y = x? – 2 and the line y = 2x + 1.

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Q: Find the area between the curves. x= - 5, x = 3, y = 2x2 + 12. y = 0 The area between the curves is…

A: Given :y=2x2+12x=-5 to x=3

Q: Find the area between x = y2, x - axis, x =y +2 To find the intersect points

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Q: Find the area of the shaded region. y = X - 3 (16,1) 16 (e,-3)

A: We first find where the curve cuts the x-axis

Q: Find the area bounded by y = x+ 4 and y = x2 - 2. Answer:

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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 bounded by the parabola y^2 =4x and the line y=2x-4 * 9 sq. units 21 sq. units 11 sq.…

A: The area of the region bounded by the curves is defined as the integral of the upper curve minus the…

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: 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 +…

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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: Find the area of the shaded region. y y= xV4 x y=0 2 y= 0 -2 SQuare units 21

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Q: Find the area of the region bounded by the x-axis and the curve below (Show all steps). y = 3x° +…

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Q: Find the area between the curves y? = -12x and y? = - 24x – 36.

A: y2=-12x,  y2=-24x-36 find intersection points -12x=-24x-36 -12x+24x=-36 12x=-36 x=-3 . y2=-12x…

Q: Find the area enclosed by the given curves y= x?,y = x 2 + 6, x = -2, and x = + 2 32 16 4 O00O

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

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Q: Find the area of the region bounded by y²= 8x and ? = x please include graph and solution

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Q: Q5 / Find the area of the triangular region in the first quadrant bounded by the x-axis and the…

A: We have to solve given problem:

Q: Find the area of the shaded region. Show your complete solution. r = 0

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Q: (b) Find the area of the shaded region y=1 y=5-x^2

A: We have to compute the area bounded by the curve y=5-x2, the line y=1 and the y-axis. We will use…

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. y = x2 − 1 and y = 8 − 8x2        square units

A: Given :

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

A: y2=2x+6 and y=x-1. To find: Area enclosed by the given two curves.

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

A: Given that, The line x=y and the Parabola 4x+y2=12   We have to find Area between the Curves   As we…

Q: Q1 By sketching the graphs, find the area of the region bounded by, y = 9 – x? and x + y = 3, -3<xS…

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Find the area enclosed by the line y = x -1 and the parabola y² = 2.x + 6.

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Q: Find the area of the shaded region. y = x – 2 2+ y=V 1 2 3 4 | square units

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Q: Find the area enclosed by {x=t3/2+t+6 & y=-t2+5t-4} and the x-axis

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Q: Find the area bounded by the given curves. y = 2x - x², y = 2x - 4 Select one: A. 32 3 В. 34 С. 37…

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Q: Find the area of the region between y = 4x² and y = a? + 2.

A: Explained below

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.