Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 12.2, Problem 41PS
To determine
To set up:a double integral for the volume of the solid region.
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Problem 10
The volume of the solid obtained by rotating the region bounded by
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Problem 12
The volume of the solid obtained by rotating the region enclosed by
x=3y, y^3= x (with y>/=0)
about the y-axis can be computed using the method of disks or washers via an integral
V=∫[upper limit=b, lower limit=a]_______dy
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The volume of the solid obtained by rotating the region enclosed by
y=1/(x^3), y=0, x=2, x=7
about the y-axis can be computed using the method of cylindrical shells via an integral
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Chapter 12 Solutions
Calculus
Ch. 12.1 - Prob. 1PSCh. 12.1 - Prob. 2PSCh. 12.1 - Prob. 3PSCh. 12.1 - Prob. 4PSCh. 12.1 - Prob. 5PSCh. 12.1 - Prob. 6PSCh. 12.1 - Prob. 7PSCh. 12.1 - Prob. 8PSCh. 12.1 - Prob. 9PSCh. 12.1 - Prob. 10PS
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- Problem 8 The volume of the solid obtained by rotating the region enclosed by y=(e^3x)+3, y=0, x=0, x=0.2 about the x-axis can be computed using the method of disksor washers via an integral V=∫[upper limit=b, lower limit=a]______ dx with limits of integration a=______ and b=_______arrow_forwardProblem 10 The volume of the solid obtained by rotating the region enclosed by y=(x^2), y=2x, about the line y=0 can be computed using the method of disks or washers via an integral V=∫[upper limit=b, lower=a]____________dx with limits of integration a=________ and b=________arrow_forwardProblem 8 The volume of the solid obtained by rotating the region enclosed by y=(x^2), x=2, x=3, y=0 about the line x=4 can be computed using the method of cylindrical shells via an integral V=∫________________dx (with lower limit of a and upper limit of b) with limits of integration a=_________ and b=_________ The volume is V=________________ cubic unitsarrow_forward
- Problem 7 Find the volume of the solid obtained by rotating the region bounded by x=6y^2 =, y=1, x=0, about the y-axis.arrow_forwardProblem 11 The volume of the solid obtained by rotating the region enclosed by y=(x^2), y=6x, about the line x=0 can be computed using the method of disks or washers via an integral V=∫[upper limit=b, lower limit=a]________dy with limits of integration a=_______ and b=________arrow_forwardProblem 3 The volume of the solid obtained by rotating the region enclosed by y=21x-(7x^2), y=0 about the axis can be computed using the method of cylindrical shells via an integral V=∫_______________ dx with limits of integration a (lower limit)= and b (upper limit)= The volume is V= _______ cubis unitsarrow_forward
- Problem 6 Find the volume of the solid obtained by rotating the region bounded by y=5x^2, x=1, and y= 0 about the x-axis. V=arrow_forwardProblem 10 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=3x about the line y=9 can be computed using the method of washers or disks via an integral V=∫________________dx (with lower limit of a and upper limit of b) with limits of integration a=_________ and b=_________ The volume of this solid can also be computed using cylindrical shells via an integral V=∫_______________dy (with lower limit of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________arrow_forwardProblem 11 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=4x, about the line x=4 can be computed using the method of washers via an integral V=∫________________dy (with lower limit of a and upper limit of b) with limits of integration a=_________ and b=_________ The volume of this solid can also be computed using cylindrical shells via an integral V=∫_______________dx (with lower limt of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________ In either case, the volume is V=______________ cubic unitsarrow_forward
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