Skip to Main Content
Calculus: Differentiation and Integration, 1st Edition
book

Calculus: Differentiation and Integration, 1st Edition

by ICFAI
April 2024
Intermediate to advanced content levelIntermediate to advanced
710 pages
20h 50m
English
Pearson India
Content preview from Calculus: Differentiation and Integration, 1st Edition
Applications of Integration 15-31
Example 15.24 Find the length of the arc of parabola y
2
= 4ax extending from the vertex (0, 0) to an
extremity of the lotus rectum (a, 2a).
Solution: Here we shall apply the formula involving
dx
dy
in place of
dy
dx
, so that
Given y
2
= 4 ax
x
y
a
=
2
4
dx
dy
y
a
=
2
S
dx
dy
dy
y
a
dy
a
a
= +
= +
=
1
1
4
1
2
0
2
2
2
0
2
( )
22
2
0
2
2 2
2
2 2
2
1
2
4
4
2
4
+
= + + + +
{ }
y
a
a
y a
a
y y a
a
log

+
= +
{ }
+
0
2
2 2
2 1 2 1
a
a x dx
a
using
log .
Example 15.25 Find the length of the arc of y = ln (sin x) between
p p
4 2
£ £x .
Solution: Given curve is y = ln (sin x) where
p p
4 2
£ £x .
Thus,
dy
dx
x
x
x= =
cos
sin
cot
Therefore, the ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Differential Equations, 3rd Edition

Differential Equations, 3rd Edition

Steven G. Krantz
Quick Calculus, 3rd Edition

Quick Calculus, 3rd Edition

Daniel Kleppner, Peter Dourmashkin, Norman Ramsey
Calculus I

Calculus I

W. Michael Kelley

Publisher Resources

ISBN: 9789353948221