The volume of the solid generated by the curve y = e 2, between z = 2 and z = 6 about the a - aris is (e4-e 12) cubic units 5(-e12 +e 4) cubic units (e4+e 12) cubic units - e 12) cubic units

Q: A curve C is the boundary of a shaded region D which defined by y = 2x-4 and y = 2x in…

A:

Q: By using Green's theorem evaluate £ (Ary – y") dr + (** + 3ry) dy where C is a closed curve starting…

A:

Q: Caleulate fe xydx + 3y'dy where C is the curve in xy plane, x = y from (0,0). to (1,3).

A: Solve the integral by substituting the curve in the question.

Q: Consider F and C below. F(x, y) = (4 + 4xy²)i + 4x²yj, C is the arc of the hyperbola y = 1/x from…

A:

Q: 1. Find an equation for the tangent plane to the surface x cos z + yře*z =4 at Po(3, –1, 0)

A:

Q: 1. Let a be a positive number. Find the surface area of the solid obtained by revolving the curve…

A: We use the disk method to find the volume

Q: sin y dV, where E lies below the plane z = x and above the triangular region with vertices (0, 0,…

A: Given, the region E lies below the plane z = x and above the triangular region with vertices 0,0,0,…

Q: The region bounded by the curves y = r² and y = x³ is rotated around a. the z-axis; b. the y-axis;…

A: the region bounded by the curves y=x2 and y=x3 is rotated around  a) the x-axis b) the y-axis c) the…

Q: Find the area Inside the cardioid r=2 cos (6/3) and outside the circle of radius r = vZ centered at…

A:

Q: 1. Evaluate the integral x(у — 1) dz where C is a curve from z = 2 to z = -2 following a semicircle…

A:

Q: a. Arc length of the curve y = 4- (x-2)² 4 bordering the region R

A:

Q: For an area A in the x-y plane, in the expression I₂ = Ix+ly, the term /₂ is the: Minimum…

A: Introduction : As per definition, The polar amount of inertia is the total sum of the moment of…

Q: Fi for oec ind volume of the solid of revolution by rolahng about the -ais each regton boundad b the…

A: To calculate the volume of the given solid of revolution

Q: The volume of the solid generated by the curve y = e, between z = 2 and z = 6 about the z- azis is

A: Given: The curve is y=e-x   To determine: The volume of the solid generated by the curve y=e-x…

Q: Assuming that C is the counterclockwise oriented boundary curve of the unit square in the first…

A: It is an simple and easy question on vector calculus  Can be easily solve by use of green's theorem

Q: The circle of radius 3 centered at the origin Ex. to calculate the area of the given region.

A: Given: The region between x-axis and the cycloid parametrized byr(t)=t-sin t, 1-cos t  for 0≤t≤2π

Q: .2 y = z, -2 < z < 2 %3D (x - 2)² + 4y2 = 4

A: (b)  The given equation is y=z2, -2≤z≤2. Observe that y-coordinate will always be positive and…

Q: a The integral that represents the length of the curve 7(t) = (2/t, cos (2t3/2), sin (2t3/2)), where…

A: length of curve

Q: 3. Consider $ -y3 da + a?y dy where curve C is defined by the line segment from (-1,0) to (1,0),…

A:

Q: 3. 3) 6) X= y 〇s454 6) Find the area 0f the surface of rotation Created by ocyEd curve about the 3.…

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

Q: Jse Green's theorem to evaluate the ne integral (2tan x _cos 2y³) dx + (7⁰s y + 2x (πº where is the…

A:

Q: (b) Set up a definite integral that is equal t length of the portion of the parabola y which serves…

A: Introduction: The washer method is used to calculate the volume enclosed by two functions. In this…

Q: C is the curve given (in three parts) by the arc of the circle x2 +y? the circle y² + z² = 4, x = 0…

A: According to the given information, it is required to determine:

Q: The region between the curve y = Vxe- and the x-axis for0 <r<∞ is rotated about the r-axis to create…

A:

Q: Find the value of Jsinydx+ (xcosy-siny)dy, where Cis any curve from (2,0) to (1,n). Ca.2 Cb1 none of…

A: Green's theorem: ∫C Pdx+Qdy =∬D ∂Q∂x-∂P∂y dA where P and Q have continuous first order partial…

Q: 4. Graph the surface 1 = y² + z² by first sketching at least three cross sections in each of the 4…

A: We have to graph the surface 1=y2+z2-x24 by sketching at least three cross-sections in each of the…

Q: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis. Find the area of…

A: Given: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis.

Q: 2. Find the length of the curve over the given region. (a) r = e", 0 € [0, 2], (b) r = 8+ 8 cos 0, 0…

A: If we have a curve r=fθ then the length of the curve for θ∈a,b is L=∫abfθ2+dfθdθ2dθ Part(a) We have…

Q: 2. Show that the surface area of the solid of revolution obtained by revolving the curve y = 1/x, x…

A:

Q: 1. Let a be a positive number. Find the surface area of the solid obtained by revolving the curve…

A:

Q: Sketch the region enclosed by the given curves. y = 2 cos(6x),    y = 2 − 2 cos(6x),    0 ≤ x ≤ π/6

A: Find the intersection points:

Q: (6) Suppose the closed curve C in R? starts at the point (-1, 1), goes along the parabola y = r? to…

A:

Q: i) The area of the surface obtained by the rotating the curve y=V 16-x², -1s×<1 about the x-axis is

A: As per the company's guidelines, we are supposed to solve first question for you,  kindly repost the…

Q: An equation of the tangent plane to the surface x = 3 y2 - z2 at the point (8, –-2,2) is: %3D (A) (x…

A:

Q: Find the area enclosed between the parametric curves x=2t^2 + 6 y=e^-5t and x-axis for t greater…

A:

Q: 3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y…

A:

Q: 7 sin(æ), æ = T, I = 27 and The region R in the first quadrant of the xy-plane is bounded by the…

A:

Q: The volume of the solid generated by the curve y = e", between a = 2 and a = 6 about the a – aæis is…

A:

Q: The volume of the solid generated by the curve y = e², between z = 2 and z =7 about the I - azis is…

A: Given curve is y=e-x  x=2 and x=7 about the x axis find the volume

Q: Given the curve z = √a² - y² over the interval 0 ≤ y ≤a/2, f d the surface area of the solid formed…

A:

Q: the surface area of a .17 rotating the curve y = x power 3 around the x - axis between the points…

A:

Q: 1) The plane of 2 = x*+y² X+y+2 = 12 and %3D inter sect along d para boloid Find the curve. lowest…

A:

Q: Starting from the point (-4, 5, 4) reparametrize the curve r (t) = (-4- 3t)i + (5 – 3t)j + (4 + 2t)k…

A:

Q: Find the area of the surface generated by -y + e revolving the curve x = 2 Osys In 7 about the…

A:

Q: Integrate h(x, y) = (x+y)i+-x)j over the closed curve that begins at (-1, 0). goes along the x-axis…

A: Let me tell you , In this problem we are going to use Green's theorem. Note: Green's theorem is only…

Q: Starting from the point (-3, –1, 1) reparametrize the curve r (t) = (-3+ 3t) i+(-1+2t)j+ (1+ 3t) k…

A:

Q: Consider the curve, y with parameter (, and function f in 3 dimensional Euclidean space with…

A:

Q: The volume of the solid generated by the curve y = e¯ª, between x = 2 and x = 7 about the x – axis…

A: Given curve, y=e-x x=2  and   x=7

Q: 4. The curve y = V4 - x for -1, 1], is an arc of the circle x2 + y2 %3D = 4. a) Find the arc length…

A: