Consider a region R bounded by the y-axis, the line segment y=8-x for x from 0...

Consider a region R bounded by the y-axis, the line segment y=8-x for x from 0 to 8, and part of the circle y=-sqrt(64-x^2) for x from 0 to 8. Find the centroid.

Expert Solution

Please do like the answer ????

Colby Messinger answered 1 year ago

let R be a region bounded by x = 0 and x =1 and y =...

let R be a region bounded by x = 0 and x =1 and y = 0 and y = 1. Suppose the density is given by 1/y+1.Notice that R is denser near the x axis. As a result we might expect the centre of mass to be below the geometric center(1/2,1/2). Also since the density does not depend on x we do expect moment of inertia about the x axis to be 1/2. verify the moment of inertia about...

let R be the region bounded by the line y=0, by the upper part of the...

let R be the region bounded by the line y=0, by the upper part of the circle x2+y2=4, and by the upper part of the circle x2+y2=9. Find the circulation of the force F= ( 5cosx-y3)i+ (x3+ 4x+ 5siny)j around the curve C , where C is the boundary curve of the region R , oriented counterclockwise. Draw the region R precisely, and show the orientation of the curve C by putting arrows on C

Let R be the region enclosed by the x-axis, the y-axis, the line x = 2...

Let R be the region enclosed by the x-axis, the y-axis, the line x = 2 , and the curve ? = 2?? +3? (1) Find the area of R by setting up and evaluating the integral. (2) Write, but do not evaluate, the volume of the solid generated by revolving R around the y-axis (3) Write, but do not evaluate the volume of the solid generated by revolving R around the x-axis (4) Write, but do not evaluate the...

The region bounded by y=(1/2)x, y=0, x=2 is rotated around the x-axis. A) find the approximation...

The region bounded by y=(1/2)x, y=0, x=2 is rotated around the x-axis. A) find the approximation of the volume given by the right riemann sum with n=1 using the disk method. Sketch the cylinder that gives approximation of the volume. B) Fine dthe approximation of the volume by the midpoint riemann sum with n=2 using disk method. sketch the two cylinders.

Consider the region bounded by cos(x2) and the x−axis for 0 ≤ x ≤ ?(π/2)^1/2 ....

Consider the region bounded by cos(x2) and the x−axis for 0 ≤ x ≤ ?(π/2)^1/2 . If this region is revolved about the y-axis, find the volume of the solid of revolution. (Note that ONLY the shell method works here).

a) Find the area of the region bounded by the line y = x and the...

a) Find the area of the region bounded by the line y = x and the curve y = 2 - x^2. Include a sketch. Find the volume of the solid created when rotating the region in part a) about the line x = 1, in two ways.

Consider the region R between the x-axis and the curve y = x^3 / 3 ,...

Consider the region R between the x-axis and the curve y = x^3 / 3 , between x = 0 and x = 1. (a) Calculate the surface area of the solid obtained by revolving R about the x-axis. (b) Write an integral for the the surface area of the solid obtained by revolving R about the y-axis

Consider the region R, which is bounded by the curves y=3x and x=y(4−y). (a) Set up, but...

Consider the region R, which is bounded by the curves y=3x and x=y(4−y). (a) Set up, but DO NOT SOLVE, an integral to find the area of the region RR. (b) Set up, but DO NOT SOLVE, an integral to find the volume of the solid resulting from revolving the region RRaround the xx-axis. (c) Set up, but DO NOT SOLVE, an integral to find the volume of the solid resulting from revolving the region RRaround the line x=−5x=−5.

1. Consider the region bounded by the graph of y^2 = r^2 −x^2 (a) When this...

1. Consider the region bounded by the graph of y^2 = r^2 −x^2 (a) When this region is rotated about the x-axis a sphere of radius r is generated. Use integration to find its volume V (b) Use integration to find the surface area of such a sphere 2. Find the arc length of the curve y = 1 3 x 3/2 on [0, 60] ( 3. Consider the graph of y = x^3 . Compute the surface area of...

Find the volume of the solid that results when the region bounded by y=√x , y=0,...

Find the volume of the solid that results when the region bounded by y=√x , y=0, and x=16 is revolved about the line x=16.

Question