Any one helps me please Find the volume of the solid generated by revolving the

Question

Any one helps me please

Find the volume of the solid generated by revolving the shaded region about the indicated axis. About the x-axis Find the volume of the solid generated by revolving the region bounded by y = 4ex, y = 0, x = 0, and x = ln 2 be about the x-axis. Find the volume of the solid generated by revolving the region bounded by x = 2 y ,x = 0, y = 9 about the y-axis. Use the washer method to find the volume of the solid obtained by rotating about the x-axis the region bounded by the curves y = x and y = x2. Use the washer method to find the volume of the solid obtained by rotating about the y-axis the region bounded by the curves x = 1/2y and x = y

Explanation / Answer

im doing 2

2) x=ln2 and y=4e^x intersect at

y=4*2=8.........(ln2,8)

volume = pi*{ y^2 dx =pi* { 16e^2x dx =[pi*16/2 * e^2x] from 0 to ln2

volume = pi*(8* 2^2-8) = 24*pi =75.4 cubic units

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