Find the area of the region bounded by y=−4x+ 9, y= 2x^2−11x+ 9, and the lines x=−2 and x= 5.

Q: Find the area A of the region between y = 4x +8 and y = 3x +2 over the interval [-2,3]. y= 4x+ 8 40-…

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Calculate the total area of the region bounded by the line y= 6x^2 + 9, the x-axis and the line x =4…

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Q: Sketch the region bounded by the graphs of the functions. y = x2 – 8x + 16, y = x2 – 24x + 144, y =…

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Q: Find the three areas of the region bounded by y=2x^2+10, y=4x+16 and the lines x=-2 and x=5.

A: Given: y=2x2+10y=4x+16x=−2x=5

Q: Find the area of the region bounded by the curve  y=2x2-3x+2  x axis and vertical lines x=0 and x =…

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Q: 2) a) Consider a rectangle which is on the region bounded by the lines y = x+4, y =-x+4 and X -…

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

Q: area of the region

A: Consider the given equations, y=2x2+10y=4x+16x=-2x=5 It is observed that the region is bounded only…

Q: What is the area of the region between the lines y = 7x and y = 3x from x = 1 to x = 4?

A: 1.

Q: Find the area of the shaded region. 160- (-2,152) f(x) = x* - 8x + 18x, g(x) = - 25x + 102 3,27)

A: Given: fx=x4-8x3+18x2 gx=-25x+102   From the graph it is visible that the points of intersection are…

Q: Find the area between the curves (x^2)-(y^2)=9 and the line y=2x-6

A: Recall: Area between two curves:          A=∫abf(x)-g(x) dx           OrA= ∫abUpper function-(Lower…

Q: Find the area of the region bounded by y=x^2-6x+5, y=0 and the lines x=2 and x=5

A: We have to find the area of the region bounded by y=x2−6x+5, y=0 and the lines x=2 and x=5. The…

Q: Sketch the region in the xy-plane defined by the inequalities x - 2y2 ≥ 0,   1 - x -| y| ≥ 0, and…

A: Now the graph is,

Q: Compute area of the region bounded byx2+ (y−1)2= 9 andy=x+ 1 and the (horizontal) liney= 1 (we…

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Q: Calculate the area of the plane region bounded by the function Y=X²-4X +5, and the line that passes…

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Q: (a) curves y=, y =-x², lines x=1, x=2

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Q: Consider a rectangle which is on the region bounded by the lines y=x+4 y=-x+4  and X-axis. If its…

A: Consider a rectangle which is on the region bounded by the lines y=x+4 y=-x+4  and X-axis   Let…

Q: Find the area bounded by the region y = 2x + 2 and the lines y = 1, y = 2

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Q: Find the three areas of the region bounded by y= 2x2+10, y=4x+16 and the lines x=-2 and x=5.

A: Given : y = 2x2 + 10, y = 4x + 16 and the lines x = -2 and x = 5.   To find the three areas.

Q: Solve for the region bounded by y=9-x^2 and y=x^4.

A: To find- Region bounded by the given curves.

Q: Find the area under the curve y=2x6y=2x6 over the interval [0,3][

A: Solution

Q: A region in the xy-plane is bounded by y = 2x + 2, X = y + 2, y = -2, 2 y = 2. and

A: Given curves are y=2x+2 and x=y22+2 The limits are y=-2 and y=2 We isolate x from the first curve,…

Q: rotate the region bounded by y=2x+1, x=4 and y=3 about the line x=-4

A: Solution:-

Q: Find the number 6 such that the line y = 6 divides the region bounded by the curves y = x2 and y =…

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Q: y = 4 – x2 y = 4 – 4x - -5-

A: Definition used -             The area between two curves f(x) and g(x) -…

Q: Find the area of the region bounded by y=2x2-3x+2 the x axis and the vertical lines x=0 and x=2

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Q: Sketch the region bounded by the graphs of the functions sec"(). y - 9 -,- -1, x1 ALA 10 10

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Q: What is the area of the region bounded by y = x^2, the x-axis, and the lines x = 2 and x = 5, using…

A: Given function is, y=x2 Limits for x is, x1=2x2=5

Q: Find the area of the reglon bounded by the graphs of the equations. y = 5x +5, x = 0, x = 2, y = 0

A: Required area is…

Q: Draw the diagram of the region bounded by y=2x+1, x+y=7 and x=

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Q: The bounded by y= xx*+1, area of the region axis. y=x, x-- 3, and

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Q: Sketch the region bounded by the graphs of the functions. y = x2 - 4x + 4, y = x2 - 12x + 36, y = 0

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Q: find the total area of the region between the graphof ƒ and the x-axis. ƒ(x) = 1 - √x, 0 ≤ x ≤ 4

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Q: (Set upintegrd for th velume ceboud X- -I y. x2 and

A: I use shell method to find volume about line x= -1

Q: The region is bounded by the curves y = x² and y = 4x - x² and is rotated about the line X = 4. %3D…

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Q: There is a line through the origin that divides the region bounded by y = x − x^2 and the x-axis…

A: Area between curves

Q: Find the three areas of the region bounded by y= 2x2+10, y=4x+1 and the lines x=-2 and x=5.

A: Given: y=2x2+10y=4x+1x=-2x=5……1   To find: Area of the region enclosed with the above curve and…

Q: Find the area of the region bounded by the curve y^2 = 4x and the lines x = 1 and x = 4.

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Q: Find the area of the shaded region. Ay 81- y= 81-x 63- 45- 27- 9- -9 -7 -5 -3 -9 1 3 5 7 9 11 -27-…

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Q: Find the area bounded by the curve y = 4x - x2 and the lines x = 0 and y = 4.

A: topic - area bounded by curves

Q: The area bounded by the curves y = 1 -x2 and y = - x2 + 2 x + 3 , line x = -1 and x = 1 is

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Q: While evaluating the area of the region bounded by two curves y√=xy=x and y−15x+54=0y−15x+54=0, the…

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Q: y = 2x 2 − 8x + 12 and y = −2x + 12.

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

A: Given: y = 9 - x2,  y = 0 To find: The value of b such that the line y = b divides the region…

Q: Find the area of the shaded region. Ay 121- y 121-x 99- 77- 55- 33- 11- -11 -9 -7 -5 -3-11 3 5 7 9…

A: The given figure is: Find the area of the shaded region.

Q: Find the area of the region that is completely bounded by the two curves f(x) equals -X^2-3X +20 and…

A: We have to solve

Q: Consider the region in the first quadrant bounded by y=x^2, the y-axis, and y=4. -the y-axis using…

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Q: Find the region bounded by y=2sqrt(x-1), the x-axis, the line x=5 and the line x=17.

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Q: find area between line y=-2+x and y=x^(1/2) and x-axis

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Q: Find the areas of the regions enclosed by the curves and lines x = 4 - y2, x = 0

A: The area of the regions enclosed by the given curve x=4-y2 and the line x=0 is shown in the figure…

Q: y=√x, x = 4, and the x-axis.

A: Consider the given function y=xand the x-axis

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.