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
15-6  Calculus – Differentiation and Integration
=
[ ]
+
[ ]
= + =
cos cos
.
x x
0
2
4
p
p
p
2 2
Example 15.5 Find the area of the region bounded by the curves
y x
2
10= and y x= +2 .
Solution: Given curves are y x
2
10= and y x= +2 .
For simplification, we rewrite the curves as x y x y= = 10 2
2 2
, ( ) .
The points of intersection are
10 2
10 4 4
2 4 6 0
1 3
2 2
2 2
2
=
+ = +
=
= =
y y
y y y
y y
y y
( )
and
Also note that the area to be computed is bounded above by the curve
y x
2
10=
and bounded below
by y x= +2 .
The required area is given by
( ( ) ( )) ( ( ) )
( )
f y g y dy y y dy
y y y dy
a
b
=
= +
10 2
10 4 4
2 2
1
3
2 2
1
3
∫∫
= +
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