AB Module 8 DBA: This is a non-calculator assignment. Please show all your work to support your answers. The graph of f(x) = 8-x³ and the line / which is tangent to f at x = 1 is shown in the figure below. The equation for line / is y=-3x + 10. Region R is the shaded region between line I, the graph of f and the y-axis while S is the shaded region between line I, the graph of f and the x-axis. y R (1,7) y=8-x' line / S (a) Find the area of the shaded region R. (b) Region R is the base of a solid. For this solid, each cross-section perpendicular to the x-axis is a semi-circle. Write, but do not evaluate, an integral expression that would compute the volume of the solid. (c) Region S is rotated about the y-axis. Write, but do not evaluate, an integral expression that would compute the volume of the solid. (d) In quadrant 1, the region formed by x-axis, y-axis and f(x) is rotated about the x-axis. Write, but do not evaluate, an integral expression that would compute the volume of the solid.
AB Module 8 DBA: This is a non-calculator assignment. Please show all your work to support your answers. The graph of f(x) = 8-x³ and the line / which is tangent to f at x = 1 is shown in the figure below. The equation for line / is y=-3x + 10. Region R is the shaded region between line I, the graph of f and the y-axis while S is the shaded region between line I, the graph of f and the x-axis. y R (1,7) y=8-x' line / S (a) Find the area of the shaded region R. (b) Region R is the base of a solid. For this solid, each cross-section perpendicular to the x-axis is a semi-circle. Write, but do not evaluate, an integral expression that would compute the volume of the solid. (c) Region S is rotated about the y-axis. Write, but do not evaluate, an integral expression that would compute the volume of the solid. (d) In quadrant 1, the region formed by x-axis, y-axis and f(x) is rotated about the x-axis. Write, but do not evaluate, an integral expression that would compute the volume of the solid.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The graph of f(x) = 8-x^3 and the line l which is tangent to f at x =1 is shown in the figure below....
Transcribed Image Text:AB Module 8 DBA:
This is a non-calculator assignment. Please show all your work to support your answers.
The graph of f(x) = 8-x³ and the line / which is tangent to f at x = 1 is shown in
the figure below. The equation for line / is y=-3x + 10. Region R is the shaded
region between line I, the graph of f and the y-axis while S is the shaded region
between line I, the graph of f and the x-axis.
R
(1,7)
y=8-x²
line /
S
(a) Find the area of the shaded region R.
(b) Region R is the base of a solid. For this solid, each cross-section
perpendicular to the x-axis is a semi-circle. Write, but do not evaluate, an
integral expression that would compute the volume of the solid.
(c) Region S is rotated about the y-axis. Write, but do not evaluate, an
integral expression that would compute the volume of the solid.
(d) In quadrant 1, the region formed by x-axis, y-axis and f(x) is rotated about
the x-axis. Write, but do not evaluate, an integral expression that would
compute the volume of the solid.
ter
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