3. The base of a solid is the region bound by y = sin(x) and the x-axis from x =0 to x = T. Each cross- sectional cut, perpendicular to the x-axis, is an equilateral triangle sitting on this base. (a) Find the equation for A(x), the area of each cross-sectional cut. (b) Set up and solve the definite integral for volume of this solid. (Hint: you will need the identity sin (x)=[1-cos(2x)] to evaluate the integral.)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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3. The base of a solid is the region bound by y= sin (x) and the x-axis from x =0 tox = T. Each cross-
%3D
sectional cut, perpendicular to the x-axis, is an equilateral triangle sitting on this base.
(a) Find the equation for A(x), the area of each cross-sectional cut.
(b) Set
up
and solve the definite integral for volume of this solid. (Hint: you will need the identity
sin (x)=[1- cos(2x)] to evaluate the integral.)
Ax
y = sin x
sin x
Transcribed Image Text:3. The base of a solid is the region bound by y= sin (x) and the x-axis from x =0 tox = T. Each cross- %3D sectional cut, perpendicular to the x-axis, is an equilateral triangle sitting on this base. (a) Find the equation for A(x), the area of each cross-sectional cut. (b) Set up and solve the definite integral for volume of this solid. (Hint: you will need the identity sin (x)=[1- cos(2x)] to evaluate the integral.) Ax y = sin x sin x
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