Find the volume of the solid obtained by rotating the region bounded by the give

Question

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

y=lnx, y=2,y=3,x=0; about the y-axis

answer as much as possible show work to get points

6) An aquarium 3 m long, 6 m wide, and 1 m deep is full of water. Find the work (in J) needed to pump

half of the water out of the aquarium. (Use the facts that the density of water is 1000kg/m^3 and g=9.8m/s^2

)

5) Graph the region between the curves and use your calculator to compute the area correct to five decimal

places.

y=2e^1-x^2, y=2x^4

7) Find the volume of the solid obtained by rotating the region bounded by y=x^1/3 about the

line

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the

given curves about the specified axis.

y=x^4,y=0,y=1; about the line x=2

Find the average value of the function f(t)=t sin(t^2) on the interval .[0,20]

the linear density of 15m long rod is 22.5/radical(x+1) kg/m, where x is measured in meters from one end of the rod. find the average density of the rod.

Explanation / Answer

[ 2? radius height thickness ] integral , radius is [ x -0] , height is [ ?(2x) - x/2] , x in [ 0 , 8] , thickness is [ dx ]..

[ ? ( large radius

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