calculus
posted by maria
The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.
y = −x2 + 7x − 12, y = 0; about the xaxis

Steve
y = (x3)(x4)
So, using discs of thickness dx,
v = ∫[3,4] πr^2 dx
where r=y
v = ∫[3,4] π(x^27x+12)^2 dx = π/30
Using shells of thickness dy, and taking advantage of the symmetry,
v = 2∫[0,1/4] 2πrh dy
where r=y and h=√(1/4  y)
v = 2∫[0,1/4] 2πy√(1/4  y) dy = π/30 
cynthia
A variable force of
7x−2
pounds moves an object along a straight line when it is x feet from the origin. Calculate the work done in moving the object from
x = 1
ft to
x = 19
ft. (Round your answer to two decimal places.)
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