Use any method to find the volume, V, of the solid obtained by rotating the region enclosed by the curves about the given axis. y² = x¹, x = 1, x = 6, axis y = -6 (Express numbers in exact form. Use symbolic notation and fractions where needed.) V = Incorrect (156+24√√6 +In(6))ñ

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Use any method to find the volume, V, of the solid obtained by rotating the region enclosed by the curves about the given axis.
y² = x¯¹, x = 1,
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
X = 6, axis y = −6
V = (156+24√√6 +ln(6))π
Incorrect
<
Feedback
You have not correctly calculated the
volume of the solid.
Slice the region vertically and use the
washer method to find the volume of
the solid of revolution.
b
[*(Router - Riner) dx
a
V = π
X
Note that a and b are the x-coordinates
of the intersection points.
Find Router as the distance from the
axis of rotation to the top point of the
region. Find Rinner as the distance from
the axis of rotation to the bottom point
of the region.
Transcribed Image Text:Use any method to find the volume, V, of the solid obtained by rotating the region enclosed by the curves about the given axis. y² = x¯¹, x = 1, (Express numbers in exact form. Use symbolic notation and fractions where needed.) X = 6, axis y = −6 V = (156+24√√6 +ln(6))π Incorrect < Feedback You have not correctly calculated the volume of the solid. Slice the region vertically and use the washer method to find the volume of the solid of revolution. b [*(Router - Riner) dx a V = π X Note that a and b are the x-coordinates of the intersection points. Find Router as the distance from the axis of rotation to the top point of the region. Find Rinner as the distance from the axis of rotation to the bottom point of the region.
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