rotate around the z -axis the region :T ={(x,z)'∈ R^2:sin z<x<π -z,0<z<π} to obtain the solid...

rotate around the z -axis the region :T ={(x,z)'∈ R^2:sin z<x<π -z,0<z<π} to obtain the solid Ω.find its volume and center of mass.

Expert Solution

Colby Messinger answered 2 years ago

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).

Consider the spiral path x(t) = (cos^2t,sin^2t,t) for 0 ≤ t ≤ π/2. Evaluate the integral...

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

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f(x,y)=sin(2x)sin(y) intervals for x and y: -π/2 ≤ x ≤ π/2 and -π ≤ y ≤...

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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...

Consider the parametric equation of a curve: x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π...

Consider the parametric equation of a curve: x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π Part (a): Find the Cartesian equation of the curve by eliminating the parameter. Also, graph the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. Label any x and y intercepts. Part(b): Find the point (x,y) on the curve with tangent slope 1 and write the equation of the tangent line.

y''(t)+(x+y)^2y(t)=sin(xt+yt)-sin(xt-y*t), y(0)=0, y'(0)=0, x and y are real numbers

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1. Express the function f(t) = 0, -π/2<t<π/2 &nbsp

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Find the volume of the solid obtained by revolving the area under y=cosx on [0,π/2] around the y-axis. The total weight of a cable hanging from the ceiling plus the bucket of coal it is attached to is F(x)=1800−2x pounds when the bucket is xx feet off the ground (the cable gets shorter as the bucket is lifted, so the weight decreases). Find the total work done in lifting the bucket from the ground to 100 feet off the ground.

1.The domain of r(t)=〈sin(t),cos(t),ln(t+1)〉 is Select one: a. (−∞,−1] b. (π,2π) c. (−∞,−2] d. (−π,2π) e....

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