f(x, y) - x/y over the region in the first quad- rant bounded by the lines y = x, y = 2x, x = 1, x = 2

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = •[ f(x) dx + [90 g(x) dx,…

A: First we identify the region by plotting (sketching) it.

Q: 8. The region of integration D is bounded by the lines y = x,x + y ==,y = 0. Show that 1 | sin(x +…

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Q: Express integral I y + x (-4x-2y) -0,x= 1 and y=0,y-1-xto T. of u- dydx in terms of (u)and (v) given…

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Q: Let R be the region bounded by the curve y = r and the line y = 2x. Use inequal- ities to describe R…

A: In this question we have to describe the area of region by using vertical cross section

Q: The area of the region bounded by the curves y =x and y = 20 –x² is drx|-'א-0 'J - »4,4 - S** |20…

A: We will use double integration to find area

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

A: The area between the curves y=9-x2, y=x, x=0 :The area between curves is the area between a curve fx…

Q: The area of the region bounded by the curves y =x and y = 20-x² is =J 120-x² -x| dr -5 попе 4.4 A =…

A: First find out the intersection points of both the curves than integrate.

Q: Sketch the region R of integration and switch the order of integration. V 64 - x2 f(x, y) dy dx 5 X…

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Q: 2. Region bounded by y= x, x=0 and y=15, rotated about the y-axis

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Q: Find the area of the bounded region by the equation y= x+4 , Y - -4 y- ayis and the x-axir.

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Q: The region between y=x+3 line and yax+l curu a) x -axis 6) y=1 line cX=-1 line

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Q: The region bounded by y = v9– x² and y = 0 has an area of . Find the y-coordinate of its centroid.

A: Suppose the region is bounded by fx and gx on a,b where fx≥gx .Assume centroid is denoted by x¯,y¯…

Q: Integrate f(x, y, z) = x over the region in the first octant (x 2 0, y 2 0, z 2 0) above z = y2 and…

A: Given that,

Q: Compute area of the region bounded byx2+ (y−1)2= 9 andy=x+ 1 and the (horizontal) liney= 1 (we…

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Q: Determine the area of the region bounded by 3x - 5y + 4 = 0 and y-axis from y = 2 to y = 5.

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Q: Find the area of the region bounded by the curve 2-4r and the lines x = 1 and x = 4.

A: To find the area

Q: 2. The region bounded by x = 2 y, x = 0, y = 9 is rotated about the y - axis.

A: Given Data: The given curve is x=2y. Rotated about y axis. The limit for y axis is (0, 9).

Q: Let R be the region bounded by the curve y = x and the line y = 2x. Use inequal- ities to describe R…

A: To describe: The region R using inequalities in terms of its vertical cross-sections. Calculation:…

Q: The region R is bounded by y 4 %3D and y = x +3. -

A:

Q: under the cone Z =Vx²+y² and above the region bounded by the semicircle X=-V 4-y and the y-axis.

A: The circle and a cone is given as,

Q: The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e²…

A: Solution

Q: Integrate f (x, y) = x over the region bounded by y = x, y = 4x − x^2, and y = 0 in two ways: as a…

A: First draw the graph of line y=x and parabola y=4x-x2. Then find the area of the intersection…

Q: Given y = 3x –- 2x +1, y =-x² + 2x +1 and a straight line y = 0.5x ; where x>0, 1. Sketch the curves…

A: Given y=3x3-2x2+1  , y=-x2+2x+1 and a straight line y=0.5x. We need to : 1) Sketch the curves and…

Q: 4. Region bounded by y = x2, x=0 and y=15, rotated about the y-axis

A: Imagine the plot and rotate it about the axis specified and the resulting figure will lead to the…

Q: rotate the region bounded by y=2x+1, x=4 and y=3 about the line x=-4

A: Solution:-

Q: 1) Find the centroid of the region that is bounded by the line Y = 3X, the line X = 2 and the X…

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Area region = [ f(x) dx + √ [*g(x) dx…

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Q: The region lying underneath the graph of f(x)=2x^3 over the interval [0,4] has centroid

A: given: f(x)=2x3     [0,4]

Q: graph of the region of integration. • 3x/4 : | f(r,0) r dr do ? v 1. A в 7/4 2x ? v 2. 2 3x/4 ? v 3.…

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Q: The region is bounded by y = x³, y = 2x + 4 and y=-1. Then Arearegion= = ["f(x) dx + ["g(x) [*g(x)…

A: The region is bounded by y=x3, y=2x+4 and y=-1. Then Arearegion=∫abfx dx+∫bcgx, where a<b<c.To…

Q: Find area of the region bounded by x2 + y2 = 32, 6y = -6x and 20y = 6x where y 2 0. Leave your…

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Q: The centroid of the region bounded by sin x < y< cosx, and 0<x<7/4 is, TV2-4 b) 1 1 a) 4(42 +1) 4(v2…

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Q: Determine the absolute maximum and minimum values of f(x, y) = 2+4x–2x²+4y-y² on the region R…

A: The region bounded by the x-axis,y=3x and x=2 is:

Q: Find the centroid of the region bounded by the graphs of the inequalities

A: Given information: y≤14x2          ...(1)x-42+y2≤16              ...(2)y≥0                ...(3)

Q: 4. Region bounded by Y = x rotated about the y-axis ,x%30 and y=15,

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Q: Find the centroid of the region bounded by the given curves. y = 6 sin(5x), y = 6 cos(5x), x = 0, X…

A: In the question we have to find centroid of the region.

Q: The path C is a line segment of length 15 in the plane starting at (3,4). For f(x,y)=4x+3y,…

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given, y2=4-xx=0

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given,    y = x,  y = 4  and  x = 0 So the region bounded by these curves is given by shaded region…

Q: 0otained by rotating the region bounded by the given curves about the specified line y=x, y= 27, x-…

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Q: 1- Integrate The furction F(X,y= over The region bounded byrj=X7y=2x9 x =1/X=?

A: According to our company guideline if multiple questions are posted we must do only first. You can…

Q: Find b such that the line y = b divides the region bounded by the graphs of the two equations into…

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Q: R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

A: Given regions are, y=x2y=4x-x2y=0 Now, using Washer method by the formula, V=π∫abR2-r2dx

Q: 2. Find the coordinates of the centroid of the the region bounded by f(x) = x – x² from x = 0 to x =…

A: Question 2Here we have to find the centroid of the region bounded by f(x)=x-x2; x = 0; x = 1.First…

Q: Q3. The region bounded by the curve y x² and the line y 3x, is revolved about the line x = -3. Find…

A: Here i use cylindrical shell method to find out volume of rotation

Q: Find the centroid of the region bounded by the graphs of the equations using any method y = √(1 −…

A: Consider the given equations y=fx=1-x2y=gx=0 First, find the point of intersection of the given…

Q: Q3. The region bounded by the curve y = x² and the line y = 3x, is revolved about the line x = -3.…

A: We will find this using formula. As per our guidelines we are supposed to answer only one question.…

Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. Then Arearegion = [₁ f(x) dx + f[ g(x) dx,…

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [*^f(x) dx + [²8(x) x +…

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