Find the volume generated by rotating the region bounded by the given curves about the specified line. express the answers in exact form or approximate to the number of decimal places indicated.
find the volume of the solid generated by revolving the region bounded by the curve y = ln x, the x-axis, and the vertical line x=e². about the x-axis. (express the answer in exact form.)

Step-by-step explanation:

Given that the region bounded by x axis, x=e^2 and y = lnx be rotated about x axis

The limits of x are

Volume generated =

hey there!

12 is twice as much as 6 because 6 goes into 12 2 times.

since the rabbit is twice as tall, we should multiply the weight of the first rabbit, 0.25, by 2.

0.25 x 2 = 0.5

therefore, the 12 inch chocolate rabbit weighs 0.5 lb, or half a pound.

hope this !

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

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y

=

−

2

find the upper bound of the range.

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y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: