4. YA 3- y = x2 + 1 -3 -2 -1 0 1 2 3 X -11 Find the volume obtained when the shaded region is rotated through 360° about the y-axis.

Q: 28 The region in the first quadrant bounded by y rotate about the line x = 4x2 , 3x + y = 7, and the…

A: It is given that, the first quadrant bounded by y=4x2,3x+y=7 and the y-axis is rotate about x=-4.…

Q: 2. The region from problem #1 (that is, bounded by the curves y=7x and y=x² ) is now rotated about…

A:

Q: 2. Determine the volume of the solid obtained by rotating the region bounded by y = 4x and y = x³…

A: The volume of revolution of the area bounded by the curves y1=f1(x) and y2=f2(x)  between the limits…

Q: 2. (a) Based on the diagram 1, find the intersection points between curves y=r' and Hence, find the…

A: The point of intersection of two curves is the place where the two curves meet.y=f(x) To find the…

Q: YA y=x +3 5 4 - y = 4 13 11 -3 -2 -1 1 2 3 X Find the volume obtained when the shaded region is…

A:

Q: 2. Suppose that the triangle with vertices (-1,-1), (0, 1) and (1,–1) is revolved about the y –…

A:

Q: 15 - Which of the following is the volume of the object that occurs when the region bound by the y =…

A: We first sketch the region using a graphing calculator  The shaded region is rotating about the y…

Q: 3 14. Find the volume of the solid that results when the region bound by y = x°, x = 2 and the…

A: The given region is the region bounded by y=x3,x-axis y=0 and x=2. To find the volume when the…

Q: 2. The area of the parabola x2 = 4y – 4 cut through its latus rectum is revolved about the…

A: 2) Parabola; x2=4y-4End points of the latus rectum (-2,2) and (2,2)vertem = (σ 1)using washer method

Q: 6. Evaluate the volume generated by revolving the area bounded by the given curves using the washer…

A:

Q: 3]. , Let V = ar²h, where V the volume of a right circular cone of radiusr and height h. Show that…

A:

Q: I need help with part b) of the problem: b) Set up an integral that represents the volume of…

A:

Q: 3 27 Find the center of mass of a thin plate of constant density & covering the region bounded by…

A: Center of mass of a body is a point at which it can be considered that entire mass of body is…

Q: Now we can say that the volume of the solid created by rotating the region under y = 8e-X and above…

A: We will find out all the unknown values.

Q: y = √x y = x² 1. 0.8 0.6 0.4 0.2 0.2 y= √x 0.4 y=x² 0.6 0.8 1. 1.2 x

A: The equation of the curves are: C1: y = xC2:y = x2 Axis of Rotation: y-axis Formula Used: Washer…

Q: 2.5 Find the volume of the solid of revolution formed by rotating the area under y = 9 – x? over [0,…

A:

Q: Problem Sketch the solid whose volume is given by the iterated integral. LL*(1 - x) dy dx

A:

Q: The region from problem #1 (that is, bounded by the curves y  = 5x and y=x^2) is now rotated about…

A:

Q: 7) Suppose that y, =sinx and y, = cos x on [0,4] %3D Find the volume if the region between y, and y,…

A: First we sketch the region using a graphing calculator The shaded region is rotating about the x…

Q: 10. Find the volume of the solid whose base is bounded by the graphs of the equations given below…

A:

Q: 24 22. Find the volume generated by revolving about Ox the area bounded by the Ans. ra³. hyperbola…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: The triangular region Ω has vertices (1, 1), (2, 0), and (2, 3).

A: My=∫12∫-x+22x-1kx2dydx

Q: No calculators. Using the Shell method only, find the exact volume created by rotating the region…

A:

Q: 12 - Which of the following is the volume of the object that occurs when the region bound by the…

A: We sketch the region using a graphing calculator  The shaded region is rotating about the y axis

Q: 1 Find the volume generated when the area bounded by y=√√x and y=-x is rotated around the x-axis 2…

A: The region bounded by y=x and y=12x is rotated about the x-axis.

Q: 12 - Which of the following is the volume of the object that occurs when the region bound by the xy…

A: We sketch the region using a graphing calculator  The shaded region rotates around the y axis

Q: 5. (6') Find the volume of the solid formed by revolving the area bounded by y = sin(x²), x E [0, T)…

A: Given - A bounded region To find - Volume of solid by revolving the region about specified line

Q: y = x² +9 %3D y= 18

A:

Q: and y=2 8) x = y² +1₁ x = 0, you, The most appropriate method to use to find the volume generated by…

A: The given region is x=y2+1,x=0,y=-1 and y=2. Find the volume generated by revolving the region about…

Q: The region in the first quadrant that is bounded above by the curvey = 1/x1/4, on the left by the…

A: Given: The region in the first quadrant that is bounded above by the curvey=1x14 on the left by the…

Q: Example 8: Find the volume of the solid whose base is bounded by y = x +1 and y = x², the cross…

A:

Q: Given a curve having an equation of y2 = 4x. a) Compute the area bounded by the curve and the line…

A:

Q: 1 Find the volume generated when the area bounded by y=√√x and y=-x is rotated around the x-axis 2 A…

A:

Q: Problem 2: Use the method of cylindrical shells to find the volume when the region bounded above by…

A: Here Region bounded above by x=y2 and x=2-y and below by the x axisand rotated around the x axis.

Q: 1 3) Consider the region bounded by the graphs of y =-x, y= V4-x , and y=0. 3 c) If this region is…

A:

Q: 1. Obtain the volume of the region rotated to the right of the y-axis and to the left of the curve x…

A:

Q: 1/6 Find the volume of the solid obtained by rotating the region bounded by and リー2) about the line…

A: Now , we will find the  volume of the solid  obtained by rotating the region bounded by the given…

Q: 46. Find the volume of the solid produced by rotating the region enclosed line y = -1 that is…

A:

Q: (3+In x) Find the volume of the solid when the curve y=- is rotated 360° about the x-axis between x…

A: Using disk method volume is:  V=∫ee3πy2dx     =∫ee3π3+lnx3/2x1/22dx     =π∫ee33+lnx3xdx…

Q: 1. Find the area bounded by the curve y = x^2  and the x-axis and the ordinates x = 0 and x = 2 2.…

A:

Q: 6. Find the volume of solid generated by revolving bout the y² = 4x, x = 0, y = 4 about y = 4.

A: Given curves are, which generate the solid y2=4x, x=0, y=4   Graph is Since y2=4x⇒y=4x

Q: 4) (6.) Find the volume of the solid formed from the region between y = e*, y = 0, x = 0, x = 1…

A:

Q: 6. Find the volume if the area bounded by the curve y = x3 + 1, the x-axis and the limits of x = 0…

A:

Q: Find the volume x=y-y2; x=0 revolving at y-axis

A: Given problem:- Find the volume x=y-y2 ; x=0 revolving at y-axis

Q: 4 8. What is the volume of the solid generated when the region bounded by y= V4 +3x – x and y = 2 is…

A:

Q: and a) x = y² + 1₁ x = 0, y =- y = 2 The volume generated by revolving the region about the line y=2…

A: We can solve as follows

Q: Find the volume generated by revolving about the line x - 4 = 0 the area bounded by the curve x2 =…

A:

Q: Given that the area R is limited by the curve y = x + 1, y = −x + 1 and the line y = α, 0 ≤ α ≤ 1.…

A: Given the bounded region: Rotation about x axis Volume of solid of revolution = 2π3

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.