1. (a) Use integration by parts to show that b J cos(ax) cos(bx) dx = sin(bx) cos(ax). sin(ax) cos(bx) + d where a, b are positive constants with a ‡ b, and d is an arbitrary constant. 6² - a² (b) If a planar curve in R2 is defined by the equation y = f(x), x = [a, b], then the arc length is given by the integral cb 2 dy [²√ ₁ + (12) dx a Support From the lecture slides, we know a flexible heavy cable has the shape X y = ccosh( where c is a constant. Find the arc length of the following hanging cable. Simplify your answer. 6m a 6² - a² dx. 15m Support X
1. (a) Use integration by parts to show that b J cos(ax) cos(bx) dx = sin(bx) cos(ax). sin(ax) cos(bx) + d where a, b are positive constants with a ‡ b, and d is an arbitrary constant. 6² - a² (b) If a planar curve in R2 is defined by the equation y = f(x), x = [a, b], then the arc length is given by the integral cb 2 dy [²√ ₁ + (12) dx a Support From the lecture slides, we know a flexible heavy cable has the shape X y = ccosh( where c is a constant. Find the arc length of the following hanging cable. Simplify your answer. 6m a 6² - a² dx. 15m Support X
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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![1. (a) Use integration by parts to show that
Ja cos(ax) cos(bx) dx
b
6² a²
sin(ax) cos(bx) + d
where a, b are positive constants with a b, and d is an arbitrary constant.
sin(bx) cos(ax) -
cb
2
(du)
L. √/₁ + (22) ²d₂
dy
dx.
dx
a
(b) If a planar curve in R² is defined by the equation y = f(x), x = [a, b], then the arc
length is given by the integral
Support
From the lecture slides, we know a flexible heavy cable has the shape
X
y = c cosh(), where c is a constant.
Find the arc length of the following hanging cable. Simplify your answer.
y
62
6m
a
15m
Support
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9dd77f94-a5e7-47d3-a2ba-eff6d53f0d48%2F01283652-40df-4b17-867c-660f19347347%2Fwl31bu_processed.png&w=3840&q=75)
Transcribed Image Text:1. (a) Use integration by parts to show that
Ja cos(ax) cos(bx) dx
b
6² a²
sin(ax) cos(bx) + d
where a, b are positive constants with a b, and d is an arbitrary constant.
sin(bx) cos(ax) -
cb
2
(du)
L. √/₁ + (22) ²d₂
dy
dx.
dx
a
(b) If a planar curve in R² is defined by the equation y = f(x), x = [a, b], then the arc
length is given by the integral
Support
From the lecture slides, we know a flexible heavy cable has the shape
X
y = c cosh(), where c is a constant.
Find the arc length of the following hanging cable. Simplify your answer.
y
62
6m
a
15m
Support
X
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