Download - Double integral over general region calculus
Gandhinagar Institute Of Technology
Subject : CALCULUS(210014).
Branch : MECHANICAL [KG2].
Topic : Double Integral Over General Region
Guided By : SHIKHA YADAV.
Active Learning Assignment Prepared By : MAKWANA NIRAV.
Enrollment No : 160120119048.
METHODS FOR FINDING REGION1. VERTICAL STRIP
2. HORIZONTAL STRIP
x
x=0
y=0
A B
CD
y
P Q
x
x=0
y=0
A B
CD
y
Let The Function be f(x,y)
Limit Of y Limit Of x
β«π₯=π΄
π₯=π΅
β β«π¦=π
π¦=π
π (π₯ , π¦ )β π¦β π₯
Limit Of x Let The Function be f(x,y)
Limit Of y
β«π¦= π΄
π¦=π·
β β«π₯=π
π₯=π
π (π₯ , π¦ )β π₯β π¦
P
Q
Example 1: Let the triangular region enclosed by the lines y=0, y=2x and x=1. Then find the double integration over region R and the function is β’ Here Limit of x is from to 1β’ Limit of y is from 0 to 2 (2x=2(1)=2)β’
β’
β’ =
=[ - ]
β’ I =
y=2x
x=1
o
x=o
y=o
P Q
I =
1
π¦2
2
0
Example 2: Find the region over the triangle x=o, y=0, ax+by=1 and the fuction is
β’ Limits of y : y=0 to y=.
β’ Limits of x : x=0 to x=.
β’ I =β’ = β’ = β’ [] β’ = β’ β’ () β’ I =
o
x=o
y=o
ax+by=1Q(0,)
P()
A
B
1βππ₯π
0
1π
0
I =