Bounded by the planes z= x, y =x, x+y=2 and z= 0

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: 1) Evaluate the line integral Fdr where F(x, y, =) = (x+3y, 2y +z, xy) and y: line segment from…

A: Here, F→(x,y,z)=x+3y,2y+z,xy and γ: line segment from (2,1,3) to (3,3,5) We need to evaluate ∫γF→dr→

Q: 3 - Find the bounded ly y=2x-2, x=-1, x= 2 3 area y=2X - 2, x=-I, x= 2 4- Find the anea bondol .

A: Integrate the given parabola from x=-1 to x=2

Q: An area of a region bounded by a curve y = f(x), x axis and lines x = a and y = b for (b > a) may be…

A:

Q: a) Evaluate [(2x- y' )dA over triangular region R enclosed between the lines y = -x +1, y = x+1 and…

A: Given integral is ∫∫R2x-y2dA, where R is the triangular region R enclosed between the lines y=-x+1,…

Q: /Evaluate The are bounded by The Semiellipes y =2J5-x' oP The line 6 X = ±1 ,Y=-1 %3D

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Q: Find the angle between the planes 3x – 2y + z + 4 = 0 and x + 4y – 3z – 3 = 0. Express your answers…

A: The angle between two planes is equal to the angle between their normals.

Q: Calculate FdV where F = 2i+2zj+yk and V is a space bounded by z = 0, z = 4 and x² + y² = 9. X 4 Z ΦΕ…

A: Here we can use spherical coordinate but we use peoperty of triple and double integration that it…

Q: Show the triangular region bounded by the lines x = 0, y = 0 and x + y = 1 is invariant for the…

A: Given: It is given that, the triangular region is x=0, y=0 and x+y=1. To prove: We have to prove…

Q: Let I = , zdV ,where D is bounded by the planes x = 0, %3D 6. z 0, x+y = 2 and the cylinder x2 + z2…

A: Given: I=∫∫∫D z dVwhere D is bounded by the planes x=0, z=0, x+y=2 and the cylinder x2+z2=1 in the…

Q: a) F(x,y, z) : planes x = 0, x = 1, y = 0, y = 1, z = 0, and z = 1. 3xi + xyj + 2xzk and E is the…

A: Solution of (a) is in given below

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: (6) I. adv, where E is bounded by the planes z=0, y = 0, =0, y+= =1 and +=1, as shown in the figure…

A: Given that,

Q: Let I = , zdV ,where D is bounded by the planes x = 0, z = 0, x+ y = 2 and the cylinder x2 + z2 = 1…

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = S [² f(x) dx + √° 9( g(x)…

A: Given the region is bounded by y = x3 , y = 2x+4 and y = -1. Intersection of y = x3 and y = 2x+4 is…

Q: 7. Which surface is parameterized by ř(u, v) = (u, uv, v) for –1 < u <1 and –1< v< 1?

A: r→(u, v) = u, uv, v for -1≤u≤1 and -1≤v≤1The parametric curve is  Option C is correct.

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion= = ["5(x) f(x) dx + dx +…

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Q: the voulme of the region are  bounded by the paraboloid x= y^2+z^2 and the half cone x=…

A: The volume of the region bounded by the paraboloid x= y2+z2 and the half cone x= 8y2+z2

Q: A region R consists of a square bounded by the lines x = -1, x = 1, y = 0, and y = -2 and a half…

A: The given region is as follows: The area of region is  A=∬RdA  =Area of semi-circle of radius…

Q: Let I = [[, ydV ,where D is bounded by the planes y = 0, z = 0 , x+ y = 5 and the cylinder y2 + z2 =…

A: We have to solve given problem:

Q: 3. The region bounded by y = x³, y = x, x > 0 is rotated about the x – - axis.

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Q: The value of the integral (inage 1). where C is the closed curve 4x2 + 5y2= 7, 3x + 2y − 9z = 5.

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Q: Fimd the Valume of the Solied oblaimed by nelating the where Ris bounded by y= x* -2,X=2,X=4 and y=0…

A: I have done solution step by step in detail...just go through the solution and follow the step as I…

Q: Integrate Xy ed २ over the triangular region with vertices: (0,0), ), (0,8) (0,16)

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Q: Find the area of the region cut from the plane x+4y+8z=9 by the cylinder whose walls are x=y2 and…

A: Given, x+4y+8z=9 x=y² x=18−y² Therefore, The surface is  f=0 with f= x+4y+8z-9

Q: IF en Inner pYoduct Space X iS Vea show thet condition Hnll=Hyll impLies +ye X-y>0c what does this…

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Q: Find the area of the surface given by z=f(x,y)=3+x3/2 over the region R, which is the rectangle with…

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Q: Verify Divergence Theorem for by co-ordinate planes and the plane 2 x + y + 2 z = 6. F = (x+ y³) i –…

A: Given that F=(x+y2)i-2xj+2yzk The divergence theorem is, ∭FdV=∭∇Fdxdydz On surface S1, y+2z=6,…

Q: A region R consists of a square bounded by the lines x = −7, x = 7, y = 0, and y = −14and a half…

A: Draw the region R as follows.

Q: find volume 24. The region in the first octant bounded by the coordinate planes and the planes x + z…

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Q: Calculate ( (2x + y) dV , where V is a closed space bounded by the cylinder z = 4 – x? and the…

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Q: The solid bounded by z = x, z = 2 – x², z + y = 3, and y = 0

A: Volume of a solid is obtained using triple integration by the formulae =∫∫∫dx dy dz The solid is…

Q: 2. Sketch the two dimensional planar region R = {(x, y) | 0 <x < 2, x² < y < 2x}.

A: Solution Given Seetch the two dimensional planar region R={(x,y)|0≤x≤2,x2≤y2x}

Q: 4+ g(x) = x + 2 1 2 3.

A:

Q: 2. The area bounded by y = -(x - 1)2 + 4, and the lines x =1, y = 2, and y = 4 rotated about the %3D…

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Q: /Evaluate The are bounded by The Semiellipes y=25-x' oP The lines X = ±1,Y=-1

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

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Q: 4. Find the area enclosed by: a. y= sin(x) and y cos(x), x=0, x = and the y-axis. b. y=x and y =Vx.…

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Q: An _____ is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and…

A: The sum of the distances to any point on the ellipse (x,y) from the two foci (c,0) and (-c,0) is a…

Q: It is possible for a region in the xy-plane to be both type 1 and type 2 at the same time.

A: This is possible.

Q: . y = x2 and x2 = y

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: b. Draw the image of the W-plane into which the region bounded by the straight lines in the Z-plane…

A: The solution is given below

Q: 2)Evaluate er dA , Ris bounded by y = x2,y 1 3)Evaluate I| Vy2 + 1dA , Ris bounded by x = 4 - y? ,x…

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Q: find the are of the plane region bounded by the urves y=3x2 and y=16-x2

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Q: rector space over R

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Q: he region bounded by the cylinder x2 + y2 = 9 and the planes z=0 and x +z =9 O 243 O 81T 27TT 729TT

A: Follow next step

Q: Let S be the portion of the cylinder y = 1 − x2 with x≥0; y≥0, bounded by the planes z = 2, and z =…

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Q: The region in the first octant bounded by the coordinate planes, the plane y + z = 2, and the…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.