Find the area of the region R bounded by y = Vx and y = x , in the first quadrant. Sketch the graph and a representative rectangle.

Q: Find the area of the region bounded by 2x and the y-axis using the horizontal strip. 4 12 y² +1

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Q: problem in photo attached

A: Graph the functions. Shaded the bounded region by y=x^2 and y=x^4.

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

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Q: y=x² And y=-x+4¢

A: Given: y=x2   and y=-x2+4x

Q: Sketch the region enclosed by y = e, y = e, and æ 1. Find the area of the region.

A: In given question,the concept of area under the curve is applied. Area under the curve Different…

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

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Q: Sketch the region enclosed by y = e, y = e¹0, and x = 1. Find the area of the region.

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Q: Sketch the graph and find the area of the region that lies inside both r = 1 and r = 2sinθ.

A: To sketch: The graph of the equation and find the area of the region that lies inside the equation.…

Q: What is the area of the region enclosed by the curves y = x³ and x =y² ? A) B) D) E) 15

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Q: Find the area of the region bounded by the three curves y = x², x = y³, and x + y = 2.

A: It is given that, y3=x ⇒y=x13let, y=f1(x)=x13y=x2let, y=f2(x)=x2x+y=2⇒y=2-xlet, y=f3(x)=2-x   Area…

Q: Find the area of the region enclosed by x = y and a = 1. %3D

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Q: Find the area of the region bounded by y ==, y: I = 2.

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Q: Find the area of the region enclosed by r = y² and y = x – 2.

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Q: Find the area of the region in the 1 quadrant bounded by y = x2 + 1, y = 1 – x², and x = 1.

A: The given equations of the curve are y=x2+1, y=1-x2 and x=1. Compute the area bounded by the above…

Q: Find the area of the region bounded by y = x', x = y°, and æ + y= 2. = x²,

A: Given: y=x2 ,x=y3 and x+y=2 Graph:

Q: Sketch the region enclosed by y = e, y = e>", and x = 1. Find the area of the region.

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Q: Sketch the region enclosed by y=e^4x,  y=e^6x, and x=1 Find the area of the region

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Q: y = x and y = x²

A: We will use simple Integration rules to find the area of the region bounded by the curves y=x and y=…

Q: Sketch the region enclosed by y = eš", y = e4", and x = 1. Find the area of the region.

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Q: Determine the area of the region bounded by æ = y? – y – 6 and a = 2y+ 4.

A: Area between two carves = double integration of (dx dy) From given two carves we will find limits of…

Q: Find the area of the region in the first quadrant enclosed by y = Vx, y = 2 – x and y = x².

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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: Find the area of the region enclosed between the curves y= x³ and x= y ?

A: Given: y=x3 and y=x

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: Find the area of the region enclosed by x = y and x = Vy– 6.

A: The graph is shown below:

Q: Sketch the region enclosed by the given curves and find its area: y = (x – 3)2, y = x + 3.

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Q: sketch the region enclosed by the curves y=x^2 , and x=y-3 , and then find its area

A: Given: y=x2  and x=y-3

Q: Find the area of the region R enclosed by the curves y = x3 and y = x3

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Q: Find the area of the region bounded by y O and Y – 8x8 + x°. -

A: First find intersection point of y=0 and y=-8x8+x9 by equating each other  ∴ -8x8+x9=0…

Q: Find the area of the shaded region 14 LA bounded above by y = 2, bounded b TE lo 1)

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Q: Find the area bounded by the two curves y = Vx and y = x².

A: The area between two curves f(x) and g(x) is given by A=∫abf(x)-g(x)dx f(x)=x2 and g(x)=x…

Q: Find the area for the region in first quadrant bounded by y2 = 6x , x = 6 and y = 0

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: Find the area of the region that is bounded by the given curve a

A: Given, r=e-θ6, π2≤θ≤π

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

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Q: Find the area of the region R bounded by y = 3√x and y = x, in the first quadrant. Sketch the graph…

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Q: Find the Area of the region enclosed by Y=JT +1 and y=X, and y-axis (sketch)

A: This question is based on application of integration.

Q: Sketch the region enclosed by y = e, y = e, and a 1. Find the area of the region.

A: we have given y=e4x ,y=e8x and x=1 the region of of given functions are

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: Find the area of the region described in the following The region bounded by y = 24 Vx and y = 3x?

A: Given, y=24x & y=3x2 To find limits of x we have, y=24x =3x2⇒24x =3x2⇒8x=x2 Now squaring on the…

Q: Sketch the region enclosed by y = e", y = e*", and a 1. Find the area of the region.

A: Given  y=e4x,y=e8x and x=1 we have to find the area if region

Q: Find the area of the region enclosed by the graphs of x + (y – 1)² = 1 and 2x = -y?.

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Q: 2. Find the area of the region bounded by y = VI and y = r.

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Q: Find the area of the region in the 1st quadrant bounded by y = x2 + 1, y = 1 – x², and x = 1.

A: Given the curves and lines y=x2+1, y=1-x2 and x=1 The figure of an area of the following region is…

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

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Q: Find the area of the region in the first quadrant that is bounded by y= \x , x- axis and y=x-2.

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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 enclosed by y = e3, y = e, and z = 1. Find the area of the region.

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Q: Find the area of the region enclosed by y = x? and y = Vr.

A: We first sketch the region using a graphing calculator  y=x2 (green) y=sqrt(x) (violet)

Q: Sketch the region enclosed by the curves y = xe¬x², Find the area enclosed by the given curves. `, y…

A: Given: y=xe-x2, y=x+1, x=2 for finding area enclosed by given curve and y-axis, first we draw region…

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.