Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verity your result. (Round your answer to three decimal places.) y = x + 3 , x = 1, x = 6, y = 0

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r=…

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Q: Sketch the region bounded by the graphs of the equations and find the area of the region.

A: Given, x=cos yx=12π3≤y≤7π3

Q: Sketch the region bounded by the curve 8xe Round your answer to four decimal places. the x-axis, and…

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Q: Find the area of the region enclosed by the curves between their intersections. y= - 5x? and y = -…

A: We first sketch the region using a graphing calculator.  We find the point of intersections by…

Q: y = Vx +1; x-axis ; y-axis ; x = 8

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Q: 6. Find the area of the region enclosed by the curves x = 3 - y² and x=y_+1.

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Q: Find the area of the region bounded by the curves below. Sketch its graph and shade the region. 1.…

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Q: Find the area of the given region. Use a graphing utility to verify your result.

A: Given: To find: The area of the given region.

Q: Find the area of the region bounded by the graphs of the equations.

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Q: 6. Find the area of the region bounded by the curve r² = 16cose. . 32 sq.units . 27 sq.units B. 35…

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Q: Find the area of the region bounded by the graphs of the equations. y = 1+√√x, x=0, x= 8, y = 0…

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Q: Find the area of the region enclosed by y = 6x² and y = x² + 1. Round your answer to three decima…

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Q: In the question  given follows,use a graphing utility to graph the region bounded by the graphs of…

A: Find the region bounded by the graphs y=110xe3x, y=0, x=0, x=2. Plot the region bounded by the…

Q: Find the area of the region that lies in the first quadrant under the curve √x + √y = 1. (Draw the…

A: Let's find area under the given curve.

Q: Find the area of the given region. Use a graphing utility to verify your result. 1 + In x3 y = y 1 2…

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Q: Find the area bounded between curves (Show the figure with the rectangular strip used) x2 = y+4…

A: Area between two curves is found by taking a small strip of the intersection part and if that strip…

Q: Find the area between y=x2-x2 and y=x2. Sketch the region

A: The given curves are: y=2-x2    and    y=x2

Q: 3. Sketch the region enclosed by the curves y=-x +3x and y = x. Hence, find the area of the region.

A: We have to find the area

Q: Use a graph to find approximate x-coordinates of the points of intersection of the given curves.…

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Q: 1* quadrant area of y = (4-x)/(x+2)²

A: Given  Curve y=(4-x)/(x+2)2  To find  area bounded by curves in first quadrant

Q: Find the area of the region bounded by the graphs of the given equations. Enter your answer in exact…

A: Given :

Q: Find the area of the region described. The region bounded by y = (x-6) and y 2x- 12

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Q: Find the area of the region. Use a graphing utility to verify your result.

A: Evaluate: ∫07xx+13dx

Q: Find the area between y=x4-x2 and y=x2 . Sketch the region

A: given  y=x4-x2 and y=x2 intersection  x4-x2=x2x4-2x2=0x2(x2-2)=0x2=0   or x2-2=0x=0    or x2=2x=0…

Q: Find the area enclosed by the given curves y = 8x2 -2  and y = 9 cos(πx). You may find it useful to…

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Q: Find the area between y= x4-x2  and y=  x2 Sketch the region

A: Solve by integration

Q: 4. Find the area of the region bounded by the line y=x and the curve y=x^3. Show the region.

A: Draw the region and find intersection point then integrate

Q: Find the total area of the region between the curve and the x-axis. 13) y = x2(x - 2)2; 0 s x s 2…

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Q: Find the area of the region bounded by the curve y=x²-1 and the line y = 24! The area is

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Q: Find the area of the region bounded by y = x³ - 8 the x-axis and the y axis. 1/3 3 1/9 9

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Q: 17.Find all points where the curves y = 3r and y = r - r intersect, by solving an appropriate…

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Q: Sketch the region enclosed by the curves y = - 1+x2 and y = 5 – |x|. Find its area.

A: given curves are                                        y=-31+x2 and y=5-|x|

Q: Calculate the area of the region. Hint: integration is not needed on this problem, since the region…

A: Given The region is contained with the graphs of r=secθ,θ=π4 and θ=0.

Q: Find the area of the region bounded by the graphs of the equations. y = x - x°, x = 0, x = 1, y = 0…

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Q: Consider the region bounded by the graphs of x-B =0 and x = y -D a. Solve for the points of…

A: Given: Region is bounded by x-B=0 and x=y2-Dwhere, B=5 and D=2 To Find: a. Solve for the points of…

Q: Find the area of the region bounded by the curve y=1–÷x² and the x-axis. 9 A 4 square units (B 6…

A: SOLUTION-

Q: Find the area between x = 1- y² and y = -x - 1. Sketch the region.

A: We will use double integration to find area bounded

Q: Find the area of the given region. Use a graphing utility to verify your result. 1 + In x3 y = y 1 1…

A: The region bounded by y=1+ln x3x between x=1 to x=2

Q: 5. Use the graphing utilities to find the area of the region enclosed by the curves x = y' - 4y? +…

A: The graph of the given curves and their bounded region is :

Q: Find the area of the given region. Use a graphing utility to verify your 1 + In x3 y = y 1 X. 1 3 4…

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Q: Sketch the region between y = x2 + a - 2 and the a-axis over the interval [-5, 5]. Find the area of…

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Q: Sketch the region bounded by the curves y = (x - 2)^2 and y = x . Find the area of the region? Find…

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Q: 9) Find the area bounded by the curves y = r³ – 3x? + 2x and y = x2 – x. Your solution should…

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Q: 6. у? - бу %3D - х Y2 – 2y = x %3D

A: To find the area between the curves

Q: Find the area bounded by the indicated curves. y 2x, y 4-2x, x = 0 (x20) The area is

A: Given; y=2x^2, y=4-2x , x>0

Q: Find the area of the region bounded by the curves y = e", y = e¯, x = -2, and x = 1.

A: y=ex, y=e-x, x=-2 and x=1. The graph is,

Q: Use a graph to find approximate x-coordinates of the points of intersection of the given curves.…

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Q: (: Find the area of the region that lies in the first quadrant under the curve √x + √y = 1. (Draw…

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Q: Find the area of the region bounded by y = 6-x-x² and the x-axis 125 6 (a) A = square units 6 (b) A=…

A: The given curves are; y=6-x-x2 and x-axis or y=0.   Now find the x-intercept of the the curve…

Q: Find the area of the region bounded by the graphs of the equations x+2 Y = x = 1, x = 5, and y = 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.