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

Q: Find the area of the region bounded by the curve y=1- and the x- axis.

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Q: Sketch the region bounded by the curves x = Vy + 3 , x =y+1 and evaluate the area

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Q: Sketch the region enclosed by the curves and find its area.  y=x, y=2x, y=-x+4

A: Calculus Question

Q: Sketch the region enclosed by the curves and find its area. y = 7x ,y = 7Vx, x = - and x = 1 Enter…

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Q: Sketch the region bounded by the curves y = vx + 4 , y=x +2 and evaluate the area.

A: Given Curves are     y = x+4   and    y = x+2  first equation can also be written as  x = y2 -4 now…

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

A: Solution

Q: Find the area of the region bounded by y = ex and y = 12 − ex and the y-axis.

A: Given, y=exy=12-ex and the y-axis   Find the area bounded by the region:

Q: Sketch the region bounded by the curves x = Vy+ 8 , x = y – 4 and evaluate the area.

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Q: find the area of the region bounded by the curves y=x3 and y = x² between their intersections.

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Q: find the area of a region bounded by the curves y= x^3, y= x ln(x^2), x=1 and x=2

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Q: What is the area of the region enclosed by the curves y=e^x, y=x^2-1 and the lines x=-1 and x=1?

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Q: Find the area of the region bounded by the curves 1 y = (x+6)²¹ Y = 4 and the x-axis using vertical…

A: Given problem is :

Q: Determine the area of the region between the two curves by integrating over the y-axis. x = y² and x…

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Q: Sketch the region enclosed by the curves and find its area. 1 y = 9x² ,y = 9 Vx,x = - and x = 1…

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Q: Find the area of the region between the curves y=x^3, y=-x, and y=1

A: Area=14 sq.units

Q: Sketch the region enclosed by the curves and find its area. y = 9r° ,y = 9/ñx = andx = 1 = 9Vã.x…

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Q: Sketch the region bounded by the curves x = 3y2 and x = 12y - y2 - 5 aand find its area.

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Q: Find the area of the region bounded by the curves y = 2x^3 − x^2 − 5x and y = −x^2 + 3x.

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Q: What is the area of the region enclosed by the curve y=x^2 and the lines y=x+6, x=0 and x=5?

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Q: Sketch the region bounded by the curves y = vx – 2 , y = x – 4 and evaluate the area

A: Solve by integration

Q: Find the area of the region bounded by the curves y = 1 (x+6)²¹ į, y = = 4 and the x-axis using…

A: Explanation of the answer is as follows

Q: Find the area of the region which is bounded by y = sin x - 3, y = 3x, y-axis and x = 2. Leave your…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the area with respect to y of the region bounded by xニy+2, ×=o, y=-! and ソミ2

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Q: Sketch the region enclosed by the curves and find its area. y = 3r° ,y = 3ñx =and x = 1 = 3x² ,y = 3…

A: Topic = Application of integration  Area = 49 / 64

Q: Find the area of the region bounded by the curves y = e", y = x e", and x = 0.

A: Given curves are y=ex, y=xex Point of intersection of the curves are evaluated as follows.…

Q: Find the area of the region bounded by the curves y = 1 (x+6)²¹ y = 4 and the x-axis using vertical…

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Q: Find the area of the region which is bounded by y = sin x - 4, y = 4x, y-axis and x = 3. Leave your…

A: Area bounded by the given curves :If f(x) and g(x) be two continuous function on a,b and f(x) ≥g(x)…

Q: Sketch the region enclosed by the curves and find its area. y = x, y = 3x, y = -x + 4

A: Given; y=x, y=3x, y=-x+4   Now find the point of intersection between the line y=-x+4 & y=3x.…

Q: Find the area bounded by the curves x 2 = y − 1 and = y − 3 .

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Q: Compute the area of the region bounded by the curves y = x and y = V (Round your answer to 3 decimal…

A: Find area between the two regions using properties definite integrals

Q: Sketch the region enclosed by the given curves and calculate its area. y=4-x to the power of 2, y=0

A: The given equation is

Q: Find the area of the region between the curves y = x + 1, y = 9 – x², x = -1, and x :2. %3D Area…

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Q: Determine the area of the region bounded by the curves y = ₁, y = 2x and x = 4

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: Sketch the region enclosed by the given curves and find its area. у — y = 1/x, у — х, у—x, х>0

A: The given curve is: y=1xy=xy=14xx>0  Sketch the region enclosed by the given curves and find its…

Q: Find the area of the region bounded by the given curves. y = 3x2 In(x), y = 12 In(x)

A: Find the area bounded by these curves.

Q: Sketch the region enclosed by the given curves and find its area. x = y4,  y = square root of (2 -…

A: We first sketch the region using a graphing calculator

Q: Sketch the region enclosed by the curves and find its area. y = e*, y = e³x, x = ln 2, x = In 3 AREA…

A: Consider the curves  y=ex,y=e3xx=ln2 , x=ln 3

Q: Find the area of the region bounded by the curves x = y + 3 and y = x – 1

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Q: Find the area of the region bounded by the given curves. y = 9x In(x), y = 36 In(x) %3D

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Q: Find the area of the enclosed region bounded by the graphs of y=e^x, y=x, the y-axis and the line…

A: Here we have to find the area of the enclosed region bounded by the graphs of y=ex,y=x,the y-axis…

Q: Find the area of the region bounded by the curves y = x 2 − 3x + 5 and y = 3x + 5.

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Q: Find the area of R - region bounded by the curve y = 1/x2 and the lines y = x and y = x/8 O 1

A: Given: The curve y = 1x2 and the lines y = x and y = x8. To find: The area of the region bounded by…

Q: Find the area of the region which is bounded by y = sin x - 2, y = 4x, y-axis and x = 2. Leave your…

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Q: Find the area of the region bounded by the curve y=1. and the x-axis.

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Q: Find the area of the region which is bounded by y = sin x - 4, y = 4x, y-axis and x = 4. Leave your…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the area of the region bounded by the given curves. y = 6x2 In(x), y = 24 In(x)

A: Graph them using a graphing calculator. The graphs meet at x=1 and x=2 Blue curve is y=24ln(x) Red…

Q: Find the area of the region bounded by the given curves. y = 8 In(x), y = x In(x)

A: We first sketch the situation using a graphing calculator  y=8ln(x) (violet) y=xln(x) (black) x…

Q: Find the area of the region bounded by the curves y = x2 – 12, from below; y= 20 – x2 from above.

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Q: Sketch the region bounded by the graphs of the equations and find its area. y =x² +1; y=x+1

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Q: Find the area of the region bounded by y = 4x + 6, y = -3x +1 and x = 15. Leave your answer correct…

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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.