(e) Find the volume of the solid of revolution obtained by rotating R about the line x disks/washers and (ii) using cylindrical shells. e using (i) Section 7.2 Problem (5): Blair is using integration by parts to evaluate sec³ 3 2x dx and has chosen u = sec2 2x %3D because it is very easy to find the derivative of u. Explain in 1-2 sentences why this is a bad choice of u, and why Blair's reason for chosing u is flawed. What should Blair use for u? Explain in 1-2 sentences why your choice for u is a better. sin" x dx as sin"- x sin x dx is only useful when n is Problem (6): We have learned that rewriting sin' odd. Let's see what happens if we try this technique with an even n. Consider the integral sin “ x dx. 3 sin x sin x dx, and carry out the process that you would use Start by peeling off one factor of sin x, i.e., for an odd n until you can go no further. Explain precisely in 1-5 English sentences where you got stuck, and why this technique, combined with the Pythagorean identities and u-substitution, does not help you to evaluate this integral. Problem (7): In this problem, we will consider two methods that will allow us to evaluate integrals of the form | sin(ax) sin(bæ) dr, cos(ar) cos(bx) dx, or sin(ar) cos(bx) dr, COS
(e) Find the volume of the solid of revolution obtained by rotating R about the line x disks/washers and (ii) using cylindrical shells. e using (i) Section 7.2 Problem (5): Blair is using integration by parts to evaluate sec³ 3 2x dx and has chosen u = sec2 2x %3D because it is very easy to find the derivative of u. Explain in 1-2 sentences why this is a bad choice of u, and why Blair's reason for chosing u is flawed. What should Blair use for u? Explain in 1-2 sentences why your choice for u is a better. sin" x dx as sin"- x sin x dx is only useful when n is Problem (6): We have learned that rewriting sin' odd. Let's see what happens if we try this technique with an even n. Consider the integral sin “ x dx. 3 sin x sin x dx, and carry out the process that you would use Start by peeling off one factor of sin x, i.e., for an odd n until you can go no further. Explain precisely in 1-5 English sentences where you got stuck, and why this technique, combined with the Pythagorean identities and u-substitution, does not help you to evaluate this integral. Problem (7): In this problem, we will consider two methods that will allow us to evaluate integrals of the form | sin(ax) sin(bæ) dr, cos(ar) cos(bx) dx, or sin(ar) cos(bx) dr, COS
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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Problem 5 please
Transcribed Image Text:(e) Find the volume of the solid of revolution obtained by rotating R about the line x
disks/washers and (ii) using cylindrical shells.
e using (i)
Section 7.2
Problem (5): Blair is using integration by parts to evaluate
sec³
3 2x dx and has chosen u = sec2 2x
%3D
because it is very easy to find the derivative of u. Explain in 1-2 sentences why this is a bad choice of u,
and why Blair's reason for chosing u is flawed. What should Blair use for u? Explain in 1-2 sentences why
your choice for u is a better.
sin" x dx as
sin"- x sin x dx is only useful when n is
Problem (6): We have learned that rewriting
sin'
odd. Let's see what happens if we try this technique with an even n. Consider the integral
sin
“ x dx.
3
sin x sin x dx, and carry out the process that you would use
Start by peeling off one factor of sin x, i.e.,
for an odd n until you can go no further. Explain precisely in 1-5 English sentences where you got stuck,
and why this technique, combined with the Pythagorean identities and u-substitution, does not help you
to evaluate this integral.
Problem (7): In this problem, we will consider two methods that will allow us to evaluate integrals of
the form
| sin(ax) sin(bæ) dr,
cos(ar) cos(bx) dx, or
sin(ar) cos(bx) dr,
COS
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