Sketch the region enclosed by the given curves. Decide whether tointegrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.y =x2 - 4x, y = 2x

Q: Sketch the region enclosed by the curves e*, y = x² – 1; x = -1,x =1. Draw a typical approximating…

A: Given curves are: y=ex   and   y=x2-1    at  x=-1 and x=1 lines and their graph by approximating…

Q: Find the area of the region enclosed by the curves y=x+5, y^2=x, y=-1 and y=2

A: You need to draw the graph using the given details and find their intersection points. Then…

Q: Find the area of a region bounded by the curves y=x3, y= 2ex , x=0, and x=1

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Q: Find Find the area of the region R enclosed by the the area of the region R enclosed by the curves y…

A: Here the area enclosed by y=x5 & y=x3 is symmetric about Y-axis. For point of intersection,…

Q: 31. y = x', y= 2 – |x|

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Q: Sketch the region enclosed by the given curves and find its area. (a) 4x + y2 = 12, y = x (b) y = 3x…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Sketch the region enclosed by y = 3x and y = 6x. Find the area of the region.

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Q: 3 a. y= 2x and y =8– 4x b. y= x°, y =8, and x= 0

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Q: Consider the infinite region in the first quadrant bounded by thegraphs of y = 1/x2 , y = 0, and x =…

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Q: Sketch the region enclosed by y 5x and y = 5x. Find the area of the region.

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Q: Find the total area of the region enclosed by the curve x = y^(2/3) and the lines x = y and y = -1.

A: To determine the area bounded by the curves.

Q: Sketch the region enclosed by y = 7x and y = 3x". Find the area of the region.

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

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Q: Sketch the region enclosed by the given curves. y = Vx, y = x, X = 25

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Q: Sketch the region enclosed by the given curves. y = |8x|, y = x2 − 9 WebAssign Plot

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Q: Sketch the region enclosed by the given curves and find the area.  y = 12 − x ² , y = x² − 6

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Q: Sketch the region enclosed by y 3x and y = 4x. Find the area of the region.

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Q: Find the area of the region enclosed by the curves y=x2−2 and y=2.

A: Integration is done after calculating the intersection points of both the equations.

Q: Sketch the region enclosed by the given curves. y = Vx- 3, x- y = 3 2 3 1 3 4 -2 Find the area of…

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Q: y=x2 -4x and y=2x -x2

A: y=x2-4x and y=2x-x2 Now, draw the graph of both the curve on the same coordinate system. From the…

Q: Sketch the region enclosed by the curves y = x² and y = 4x – x² and find its area.

A: Plot the 2 curves and find the area A to be calculated. The shaded region between the curves is the…

Q: Determine the area of the given region. The region in the first quadrant bounded by y 4x and y =…

A: Equate y=4x and y=x25-x2 to obtain the interval of integration.…

Q: Sketch the region enclosed by the curves y=x+2, y=25-x^2, x=-2, and x=2. Find the area of the…

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Q: Consider the infinite region in the first quadrant bounded by thegraphs of y = 1/√x, y = 0, x = 0,…

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Q: Sketch the region enclosed by y = 2x and y 7x. Find the area of the region.

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Q: Sketch the region enclosed by the given curves. y = 8x, y =x, y = 2/x, У 6F 6F 4 1 4 У 3 3 1 3 4…

A: First of all, plot the curves y = 2/x, y = 8x and y = (1/8) x using the graphing utility.Consider…

Q: Sketch the region enclosed by y = 3x and y = 6x°. Find the area of the region.

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Q: y =x.y = x, x> 0 1 1 y : X у —х, у — —х, х > 0 4

A: we need to use integration to find area between curves

Q: y = xe¯,y = x + 1, x = 2, and the y-axis.

A: lets plot the graph of the given functions

Q: Find the area of the region enclosed by the curves y = x + 5, y² = = x, y = −1, and y = 2.

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Q: Sketch the region enclosed by the given curves andfind its area.       y +x = 3     , y = 2  x 2  ,…

A: The given curves are x+y=3 , y=2x2 and y=14x2 , x≥0. To sketch the curve and find the area. The…

Q: Determine the area of the region enclosed by the curves y=1/x, y=1/x2, and x=9.

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Q: Graph the region bounded by the curves and determine the area of the region. x = y? – 2y; x = 0

A: ANSWER :

Q: Sketch the region enclosed by the given curves. Then find the area of the region. y=x2 , y2 =x

A: Given equation curve is

Q: Find the area of the region enclosed by the curves y =x and y = 1 FIRO FIRO

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Q: Sketch the region enclosed by the given curves. y = 3x, y = 3x

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Q: Find the area of the region enclosed by the curves 4x² + y = 4 and x - y = 1.

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Q: Sketch the region enclosed by the given curves. y = 12 – x2, y = x² – 6 y 5

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

A: y1=x2-4x    and  y2=-2x

Q: Sketch the region enclosed by the given curves. Then find the area of the region. y = 3x?, y = x² +…

A: topic - area enclosed between the curves

Q: Find the area of the region enclosed by the curves y = | x²- 4 | and y = 4 + x² / 2

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Q: Sketch the region enclosed by y 6x and 4x. Find the area of the region.

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Q: Sketch the region bounded by the curves x – y = 2 and x + y? = 8, and then find the area of the…

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Q: Sketch the curves y = 8 − x^2 and x^2 and calculate the area of the regionbetween them.

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Q: Find the area of the region enclosed by the curves: y = x' – 2x², y = 2x² – 3x -

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

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Q: Sketch the region enclosed by the given curves. approximating rectangle. 3+ x y = 1 + 2/x, y = 3)

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Q: Find the area of the region enclosed by the curves: y =x', and y= 2x-x

A: Consider the curves  y=x2y=2x−x2

Q: Find the area of the region enclosed by the two curves y = 2|x| and y = x² – 3.

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Q: Sketch the region bounded by the given curves, then find the area of the region. 25 y = 23. y = x =…

A: Formula:    Area=∫abf(x)-g(x)dx We have, f(x)=25x3, g(x)=5x2, a=2, b=12

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.