Find the areas of the indicated regions. Make sure to include a sketch of these regions. (a) The region bounded by the curve x = y? and the vertical line with equation x = 4. The region bounded by the graphs of f(x) = Vx, g(x) = –2x, and h(x) = x – 2. (Hint: (Ъ) your region should lie between x = 0 and x = 4.)

Q: (13) Find the area of the region between the line y = 2x and the curve y =x² +x-2 %3D

A: The given two curves are y = 2x y = x2 + x - 2

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Q: 1. Find the area of the region enclosed by the parabola y = 2 – x² and the line y = -x.

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Q: 19) The region in the first quadrant bounded on the left by the circle x2 + y2 = 1, on the right by…

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

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Q: 2. Find the area of the region enclosed by the parabola y = 2x² and the line y = -x-1

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Q: 2. Find the area of the region bounded by the curve y = x^3 − 2x^2 − 5 x + 6, the x-axis, and the…

A: Given: y=x3-2x2-5x+6 For finding area of region bounded by given curve with x-axis and the lines…

Q: 1) Find the area bounded by curve y = xvx2 + 1 and the lines x = 0, x = 4 an %3D the x-axis.

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Q: Find the number  b such that the line  y = b divides theregion bounded by the curves y = x 2  and y…

A: Given Data The equation of curve is y=x2. The equation of line is y=4. The equation of another line…

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Q: 2. Determine the area of the region bounded by the curve y = x³ – x2 – 2x, and а. the x-axis b. the…

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Q: Find the number b such that the line y = b divides the region bounded by the curves y = 16x2 and y =…

A: Given,

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Q: Given y = 3x –- 2x +1, y =-x² + 2x +1 and a straight line y = 0.5x ; where x>0, 1. Sketch the curves…

A: Given y=3x3-2x2+1  , y=-x2+2x+1 and a straight line y=0.5x. We need to : 1) Sketch the curves and…

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Q: 3.) Find the area bounded by the curve y = 2x and y =x-4 a.) Using Vertical strips b.) Using…

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Q: Find the area of the region bounded by the curve y2-4r and the lines x = 1 and x = 4.

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Q: 10. Sketch the curve y = 7a showing clearly the behayior of the curve near its asymptotes and x+2…

A: Given  curve is y=x+2x+1.

Q: Consider the following equations. y = x2 - 4 y - -x + 3 X - 0 X - 2 Sketch and shade the region…

A: Topic = Application of derivative

Q: 1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves.…

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Q: /2y +6 5. Find the area of region bounded by the curves and *- y-1

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Q: 2. Find the area of the region enclosed by the curve =x- 4 and y = x - 2.

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Q: The area of the region between the curve y x'-6x+ 8 and the x-axis & x=0; x= 3 is given by -6x+8)kke…

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Q: 2. Find the area of the region enclosed by the parabola y = 2 - x² and the line y = -X.

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Q: Find the area of the region bounded by the curve y2=4x and the lines x = 1 and x = 4.

A: The given curve is y2=4x and lines x=2 and x=4. From the given information,

Q: 14. Find the area of the region bounded by these two curves: X = y' – 2y and x-y-4=0

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Q: find the absolute maximum and minimum values of ƒ on the region R. ƒ(x, y) = x2 - y2 - 2x + 4y R:…

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Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x –

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3/Find the area of the region ecloseed by the curves y=cost and y=0 on the intervalL A-2

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Q: 1 Find the area of the region bounded by the curve y=1--x² and the x-axis. А 8 square units 6 square…

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Q: 1. Find the area of the region bounded by the curves y = |x² - 4| and the curve y =x2 + 4 %3D

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Q: The area of the region bounded by the curves 8x =y° and 8x = 2y+y2 -2y is

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

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Q: 1.) Find the area of the region bounded by the parabola y = 2x and the line y = x - 4

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Q: Areas of regions Find the area of the following regions.

A: Given that, y=10x2-2x-24

Q: Find the area of the region bounded by the curve y = e2x - 3e* + 2 and the x-axis.

A: The region is bounded by the graph y=e2x-3ex+2 and the x-axis.

Q: Find the area of the region between the curves y=x2-1 and y= - 2x² +2 from x= - 1 to x=1.

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Q: The area of the region bounded by the 2 curves f(x) = x² + 1 and g(x) = 2x + 1 is best described by:…

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Q: Find the area of the region bounded by the graph of y = 2x2 − 3x + 2 the x-axis, and the vertical…

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Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x – 10

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Q: ) Find the number k>0 such that the region bounded by the curves y = x² and y = kx has area 9 square…

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Q: Find the value of k between –1 and 2 such that the area of the region bounded by the lines y = -x, y…

A: we know that the area of a triangle with vertices A(x1, y1), B(x2, y2) and C(x3, y3) is given by…

Q: 2. Find the area of the region enclosed by the parabola y = 2 – x² and the line y = -x.

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Q: 3. Find the area of the region bounded by the curve y = Vx – 1, the y - axis and the lines y=1 and…

A: Simplify the equation y=x-1 to obtain the expression of x. y=x-1y2=x-1x=y2+1 Draw the graphs…

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Q: 4. Find the area of the region bounded by the parabola x=y^2 +2 and the line y=x-8 *

A: Given curves are x=y2+2, y=x-8 We have to find the area bounded by this region.

Q: Find the area of the region enclosed by the curve y=x2-2 and by the line y BO 2. y=x²-2 y=2 Co

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Q: 1. Determine the area of the region under the curve y=x√(x² - 1) 2. Determine the area of the region…

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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.