Find the area of the region in the first quadrant bounded by y = 2x + 5, y = -x + 3, y = x^2 + 1 and the y - axis

Q: Find the area of the region in the first quadrant bounded by the line y=2​x x=4​ y=2/x and the​…

A: The given region is bounded in first quadrant by following curve: y=2xx=4y=2x and the x-axis.…

Q: What is the area of the region bounded by y^2 = x and y = x^3?

A: Given curve is : y2=xy=x3 To find the area of the region bounded by the curve.

Q: Find the area of the region bounded by y = -x² – 6x – 3, y= -x2 – 8x – 13, x = -5, x = -2.

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Q: find the total area of the region between the graphof ƒ and the x-axis. ƒ(x) = 1 - (x2/4), -2 ≤ x ≤…

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Q: find the total area of the region between the graphof ƒ and the x-axis. ƒ(x) = x2 - 4x + 3, 0 ≤ x ≤…

A: We first sketch the region using a graphing calculator.

Q: Sketch the graph of the curve y = x³-21x² +146x-336 Shade the area of the region bounded by the…

A: Sketch the graph of the curve y = x³-21x² +146x-336 Shade the area of the region bounded by the…

Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

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Q: of the region. bounded メニ-3, メx and y-axis.

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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: There is a line through the origin that divides the region bounded by the parabola y = 5z – 2z and…

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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: 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: Find the area of the region bounded by the graphs of the equations. y = 8 + Vx, x = 0, x = 8, y = 0

A: Let's plot the graph : consider a vertical rectangle. So limits : y → 0 to (8 + x3 )x→ 0 to 8

Q: Find the area of the region bounded by the graphs of the equations.              y = 5x2 + 2,    x =…

A: Given  The equation  is  y = 5x2 + 2,    x = 0,   x = 2,    y = 0 Formula for area under the curve…

Q: Solve by integration: Find the centroid of the region bounded by y=x3+3 and the lines x=0 and y=0.…

A: given functions are                                              y=x3+3x=0y=0…

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

A: Answer

Q: Sketch the region bounded by the graph of the equations and find the area of the region. x = y² -…

A: Solution

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 of the region bounded by the graphs of the equations. y = 7 + Vx, x = 0, x = 8, y = 0

A: Given problem is :

Q: Find the area of the region bounded by the graphs of the equations. y = 4 + Vx, x = 0, x = 8, y = 0

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Q: Find the area of the region bounded by the graphs of the given equations. y​ = 5 - x^2, y = 5 - 5x

A: Given that, Two equations are following, y = 5 - x2  and y = 5 - 5x We have to find the area bounded…

Q: What is the area of the region bounded by the y axis with lines?

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Q: Calculate the total area of the region described. Do not count the area beneath the X axis as…

A: Given: Bounded by the curve.y=1-x2And the lines x=-1 and x=2

Q: Find the area of the region bounded by the graphs of the equations. y = 7x2 + 5,  x = 0,  x = 2,  y…

A: Graph the equations. We have to find the shaded area.

Q: Find the area of the region bounded by the graphs of the equations. y = 7x2 + 3, x 0, x = 2, y = 0…

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Q: Solve by integration and please show graph: Find the centroid of the region bounded by the x-axis…

A: Given a curve y=-16+10x-x2 we need to find its find its bounds by equating y to zero. Thus we have…

Q: Find the area of region bounded by the graphs of the equations. 1. y = 5x² + 2, x = 0, x = 2, y = 0

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Q: Find the area of the region bounded by y = 2x2 + 10, y = 4x + 16, x = -3 and x = 4.

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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: The area of the region bounded by y = v9- x² , the x-axis and the line y-x in the first quadrant is:

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Q: Shade the area of the region bounded by the specified region using integration,

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Q: There is a line through the origin that divides the region bounded by the parabola y 7z 5x and the x…

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Q: What is the area of the region bounded by the parabola y^2 = 2x and the line x-y-4 = 0? *

A: See the details solution in below

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: Find the area of the region bounded by the graphs of the equations. y = 7x2 + 1, x = 0, x = 2, y = 0

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Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

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Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

A: Our objective is to find total area of the region bounded by y=2x,the x-axis,and the lines x=2 and…

Q: Find the total area of the region enclosed between the curves: 10x² +24x and =-x³ +10x² 24x

A: The objective is to find the area bounded between the curves.

Q: The square region with vertices (4, 0), (0, 4), (8, 4), (4, 8) is revolved around the line x = -8.…

A: Draw a diagram of the square. Determine the coordinates of the centroid of the square.…

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 area of the region bounded by the graphs of the equations. y = 2+√√x, x = 0, x = 8, y = 0

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

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Q: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

A: The region is bounded by the line y=6x, the x-axis, and the lines x=3 and x=6

Q: Determine the area of the region bounded by y = 2x2 + 10, y = 4x + 16, x = -2 and x = 5.

A: Following is the graph First obtain the points of intersection…

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: Sketch the region bounded by x= 4– y² and x- y=-2. Find the area of the bounded region

A: Given:x=4-y2,x-y=-2

Q: find the total area between the region y=3x^2-3, -2< x < 2 and the x axis

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Q: Find the area of the region bounded by the line y = 2x – 5 and the parabola y = x² – 4x. - -

A: Graph of enclosed region -

Q: find the area of the region bounded by the curve y=x2 - 4x+3  , x axis and the lines x=2 and x=4

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Q: a of the region bounded by y=4x-x^2 and y=x

A: the area bounded by two curves f(x) and g(x) is given by ∫abf(x)-g(x)dx now  y=4x-x2 and y=x2-2x…

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.