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

Expert Solution

milcah answered 2 years 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...

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.

Given : the plane region R is bounded by the curves ? = 0 , ?...

Given : the plane region R is bounded by the curves ? = 0 , ? = 2 , ? = 3√? 2-Compute the volume of the solid that has the region R as the (horizontal) base; vertical slices parallel to the ?-axis are squares

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.

Let R be the region bounded by the following graphs. Find the quantities below.y= (x−1)^2+ 1,y=...

Let R be the region bounded by the following graphs. Find the quantities below.y= (x−1)^2+ 1,y= 1,x= 0 a. Volume of the solid formed by rotating R about the x-axis, using the shell method. b. Volume of the solid formed by rotating R about they-axis, using the disc method.

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...

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.

Let R be the two-dimensional region in the first quadrant of the xy- plane bounded by...

Let R be the two-dimensional region in the first quadrant of the xy- plane bounded by the lines y = x and y = 3x, and by the hyperbolas xy = 1 and xy = 3. Let (x,y) = g(u,v) be the two-dimensional transformation of the first quadrant defined by x = u/v, y = v. a) Compute the inverse transformation g−1. b) Draw the region R in the xy-plane and the region g−1(R) in the uv-plane c) Use the...

9) R is the region bounded by the curves ? = x^3 , y=2x+4 , And...

9) R is the region bounded by the curves ? = x^3 , y=2x+4 , And the y-axis. a) Find the area of the region. b) Set up the integral you would use to find the volume of a solid that has R as the base and square cross sections perpendicular to the x-axis.

5). Let f : [a,b] to R be bounded and f(x) > a > 0, for...

5). Let f : [a,b] to R be bounded and f(x) > a > 0, for all x in [a,b]. Show that if f is Riemann integrable on [a,b] then 1/f : [a,b] to R, (1/f) (x) = 1/f(x) is also Riemann integrable on [a,b].

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