Sketch the region enclosed by the given curves. Decide whether to integrate 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 given curves. Decide whether to integrate with respect to r or y.…

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Q: Sketch the region bounded by the given curves, then find its area. x=y2, x=y+6

A: Here we have to sketch the region bounded by the given curves.  We have, x=y2, x=y+6

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to r or y.…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: we have to calculate area

Q: Find the exact area of the region that lies under the curve given by y = 10/2x +1, 0<x <1 %3D

A: We know the area of the region that lies under the curve  y=f(x),  a≤x≤b is given by Area =∫aby dx…

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

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Q: Sketch and shade the region y = x² – 1, hence find the total area between the given curve and the…

A: The standard form of a parabolic function is where (h, k) is the vertex. This standard form is also…

Q: Sketch the region enclosed by the following curve and find its area. x=y¹, y = √2-x, y=0

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Recall: If x=f(y) and x=g(y) are two continuous function on [a,b] and f(y)≥g(y) on a≤y≤b , then the…

Q: Sketch the region enclosed by a y²-56 and x+y=0 Decide whether to integrate with respect to x or y,…

A: Consider the curves  x+y2=56x+y=0

Q: Find the area of the region enclosed by the given curves.  y=2cos(3x), y=2sin(6x), x=0, x=π/6

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Q: Sketch the region bounded by the given curves, then find its area. 1. y = x², y = 2x

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Q: Find the area of the region bounded by the given curves. y = √x,  y= -3√x.  y= x- 2

A: It is given,Function 1: y= -3x1  OR x1 = y29                        (1)Function 2: y= x2- 2   OR x2…

Q: Sketch the region enclosed by y = eu, y = e** 2x 4x and x = 1. Decide whether to integrate with…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: The sketch below shows the area enclosed between the curves.

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region enclosed by y = e, y = e0, and a x or y. Then find the area of the region. 1.…

A: The curves which enclosed the region are y=e5x and y=e6x.

Q: Sketch the region bounded by the given curves, then find its area. y = x^2, y = 2x

A: Given,            The equation of the curves are y=x2 and y=2x.To find : Find its area.

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region enclosed by y = eº y = e⁹, and x = 1. Decide whether to integrate with respect 5x…

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

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region enclosed by y = ešª , y = es, and x = 1. Decide whether to integrate with respect…

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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: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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

A: Given y=x2 ,y=4x-x2

Q: Sketch the region enclosed by y = /x, y = 0, x = 4 and calculate its area.

A: The region enclosed by y=x , y=0 and x=4 is given by:

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Let's find.

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 curves and find its area. y = e", y = e2a, x = ln 2, x = In 3 AREA…

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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: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Given: 2y=5x ; y=4 ; 2y+3x=8 We know that, the graphical transformation; The transformation y=afx…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Find the area of the region bounded by the given curves. y= x2, y = 4x - x2

A: The given curves are,   y= x2,  y = 4x - x2

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Find the area of the region enclosed by the given curves  y = 1/4x^2 y = 2x  x+y = 3 while x is…

A: I have done solution step by step in detail...go through the solution

Q: Find the area of the region bounded by the given curves: yx = 1, y= 0 , x = 1, x= 3

A: Given: Find the area of the region bounded by the given curves: `yx=1 y=0 x=1 x=3`

Q: 23. y = 2x, y =}r

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Q: Find the area of the region R enclosed by the curves y = x ^3 and y = x^2

A: Ans;

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Sketch the region below the curve y = x – x² and above the x-axis and find its area.

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: NOTE: Refresh your page if you can't see any equations. . the first function is  . the second…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Given curves are: C1: 2y=3x                      ...............(1)C2: y = 4…

Q: Sketch the region enclosed by the given curves and find its area. y = x², y = x*

A: By using area between the curve formula, we calculate the required area.

Q: Sketch the region bounded by the graphs of the equations and find the area of the region . y = ex, y…

A: The diagrammatic representation of the area is,

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: Sketch the region enclosed by the given curves and decide whether to integrate with respect to x or…

A: This question can be solved using application of integrals to find area under curves.

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.