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 =