Free Disk & washer methods challenge Practice Problems • Learn To Be

In the figure below is a collection of eight cylindrical disks that can be used to approximate the volume of the solid created when the region bounded by

\qquad y=\ln x~~

and the

~~x

-axis, for

~x\in[2,4]\,

is rotated about the

~x

-axis.

[Note: The radius of each cylinder is taken at the right-hand endpoint of each interval. Additionally, the interval

~[2,4]~

has been partitioned into equal sub-intervals.]

Which of the following expressions is the sum of the volumes of the eight cylinders?

Choose 1 answer:

A
$\displaystyle \dfrac{\pi}4 \sum_{i=2}^4\ln \Big({2+\dfrac i4\Big)}$
B
$\displaystyle \dfrac{\pi}4 \sum_{i=2}^4\Bigg(\ln \Big({2+\dfrac i4\Big)}\Bigg)^2$
C
$\displaystyle \dfrac{\pi}4 \sum_{i=1}^8\ln \Big({2+\dfrac i4\Big)}$
D
$\displaystyle \dfrac{\pi}4 \sum_{i=1}^8\Bigg(\ln \Big({2+\dfrac i4\Big)}\Bigg)^2$
E
None of these

Disk & washer methods challenge

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