Calculus -2 H.W # 2 IBP - means Integration By Part 1. Use the disk method to find the volume of the solid formed by revolving the region bounded by the graph of f(x) = and the x-axis (about the...

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Calculus -2
H.W # 2

IBP - means Integration By Part

1. Use the
disk
method to find the volume of the solid formed by revolving
the region bounded by the graph of
f(x) =


and the x-axis (about the x-axis.
2. Find the arc length of the graph of
y =

on the interval [1, 7]
3. Use the
shell
method to find the volume of the solid generated by
revolving the region bounded by the graphs of

y = 0, x = 3 about the y-axis.
4. Evaluate

5. Integrate

6. Use
Integration by Part
to evaluate


7. Integrate (IBP method).
8. Integrate

Evaluate (No fnInt)
10.
A cable suspended between two poles takes the shape of a catenary
whose equation is given by

Where Find the length of the cable, if x and y are in
meters.



Calculus -2 H.W # 2 IBP - means Integration By Part 1. Use the disk method to find the volume of the solid formed by revolving the region bounded by the graph of f(x) = and the x-axis ( about the x-axis. 2. Find the arc length of the graph of y = on the interval [1, 7] 3. Use the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of y = 0, x = 3 about the y-axis. 4. Evaluate 5. Integrate 6. Use Integration by Part to evaluate 7. Integrate (IBP method). 8. Integrate Evaluate (No fnInt) 10. A cable suspended between two poles takes the shape of a catenary whose equation is given by Where Find the length of the cable, if x and y are in meters.
Answered Same DayDec 21, 2021

Answer To: Calculus -2 H.W # 2 IBP - means Integration By Part 1. Use the disk method to find the volume of the...

Robert answered on Dec 21 2021
117 Votes
Solution 1:
By disk method:
Area of disk is:
( ( ))
∫ (√ )


[ ]
Hence the volume is :
Solution 2:
Length of arc is:
∫√( ( ) )









∫√(

)
∫√
(

)








Let:
(

)








∫(

)










Replacing t back
[(

)


]
( )
Hence the length of arc is 7.228 units
Solution 3:
Shell strip is:
( )
Hence volume is:

*

...
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