Evaluate the double integral y^{2}dA, D is the triangular region with vert

puntgewelb5

puntgewelb5

Answered question

2021-11-21

Evaluate the double integral y2dA, D is the triangular region with vertices (0, 1), (1,2), (4,1)

Answer & Explanation

barcelodurazo0q

barcelodurazo0q

Beginner2021-11-22Added 13 answers

Step 1
Lets
Anot1954

Anot1954

Beginner2021-11-23Added 16 answers

Step 1 
Distinguish based on dxdy. Therefore, calculate B and A's equation in terms of x.
A:y=1+x 
x=y1 
B:y=mx+b 
2=(13)(1)+b 
b=2+(13)=(73) 
y=(13)x+(73) 
x=3y+7 
Step 3 
Inferred from the graph and equations are:
1y2 
y1x3y+7 
12y13y+7(y2) dx  dy  
Step 4 
12[x(y2)]y13y+7 dy  
Step 5 
12[(y2)(3y+7y+1)] dy  
Step 6 
12[(y2)(4y+8)] dy  
Step 7 
12(4y3+8y2) dy  
Step 8 
[4y44+8y33]12=[y4+8y33]12 
Step 9 
(16+643)(1+83) 
=15+(563) 
45+563=113

user_27qwe

user_27qwe

Skilled2021-11-24Added 375 answers

Step 1

We'll integrate x before integrating y. The left-hand side is x=y1, the right function is x=73y, and y[1, 2]. So

Dy2dA=12y173yy2dxdy

=128y24y3dy=113

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