Double integral over general region calculus
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Transcript of 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
∫𝑥=𝐴
𝑥=𝐵
❑ ∫𝑦=𝑃
𝑦=𝑄
𝑓 (𝑥 , 𝑦 )ⅆ 𝑦ⅆ 𝑥
Limit Of x Let The Function be f(x,y)
Limit Of y
∫𝑦= 𝐴
𝑦=𝐷
❑ ∫𝑥=𝑃
𝑥=𝑄
𝑓 (𝑥 , 𝑦 )ⅆ 𝑥ⅆ 𝑦
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 • Here Limit of x is from to 1• Limit of y is from 0 to 2 (2x=2(1)=2)•
•
• =
=[ - ]
• I =
y=2x
x=1
o
x=o
y=o
P Q
I =
1
𝑦2
2
0
Example 2: Find the region over the triangle x=o, y=0, ax+by=1 and the fuction is
• Limits of y : y=0 to y=.
• Limits of x : x=0 to x=.
• I =• = • = • [] • = • • () • I =
o
x=o
y=o
ax+by=1Q(0,)
P()
A
B
1−𝑎𝑥𝑏
0
1𝑎
0
I =