I'm trying to study for an upcoming exam but there are three Calculus problems I can't for the life of me get. I keep getting decimals and incredibly high fractions. Please help.
1. Consider the given curves to do the following.
64y=x^(3) , y=0, x=4
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 1.
2. 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 + 14x − 45, y = 0; about the y−axis
3. 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 = 8, y = x + 7/x, about the x = −2
1. Consider the given curves to do the following.
64y=x^(3) , y=0, x=4
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 1.
2. 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 + 14x − 45, y = 0; about the y−axis
3. 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 = 8, y = x + 7/x, about the x = −2
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will use " 2π radius height thickness " concepts for all integrals
#1. radius is [ 1 - y] , height is [ 4 - 4 y^(1/3) ] , thickness is [ dy ] , y in [ 0 , 1]
#2. radius is [ x ] , thickness is [ dx ] , height is [ - x² + 14 x - 45 ] , x in [ 5 , 9 ]
#3. radius is [ x - (- 2) ] , thickness is [ dx ] , height is [ 8 - ( x + 7 / x ) ] , x in [ 1 , 7 ]
integrals are easy
#1. radius is [ 1 - y] , height is [ 4 - 4 y^(1/3) ] , thickness is [ dy ] , y in [ 0 , 1]
#2. radius is [ x ] , thickness is [ dx ] , height is [ - x² + 14 x - 45 ] , x in [ 5 , 9 ]
#3. radius is [ x - (- 2) ] , thickness is [ dx ] , height is [ 8 - ( x + 7 / x ) ] , x in [ 1 , 7 ]
integrals are easy
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I got 356.6 for the 3rd
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