1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Phoenix [80]
3 years ago
6

Approximate the integral integral integral integral f(x, y) dA by dividing the rectangle R with vertices (0, 0), (4, 0), (4, 2),

and (0, 2) into eight equal squares and finding the sum Sigma 8 i = 1 f(xi, yi) where (xi, yi) is the center of the ith square. Evaluate the iterated integral and compare it with the approximation. Integral 4 0 Integral 2 0 (x + y) dy dx Sigma 8 i = 1 f(xi, yi) delta Ai = ___________ Integral 4 0 Integral 2 0 (x + y) dy dx = _____________
Mathematics
1 answer:
amm18123 years ago
7 0

Answer:

Step-by-step explanation:

Approximate the integral \int\int\limits_R {f(x,y)} \, dA by dividing the region R with vertices (0,0),(4,0),(4,2) and (0,2) into eight equal squares.

Find the sum \sum\limits^8_{i=1}f(x_i,y_i)\delta A_i

Since all are equal squares, so \delta A_i=1 for every i

\sum\limits^8_{i=1}f(x_i,y_i)\delta A_i=f(x_1,y_1)\delta A_1+f(x_2,y_2)\delta A_2+f(x_3,y_3)\delta A_3+f(x_4,y_4)\delta A_4+f(x_5,y_5)\delta A_5+f(x_6,y_6)\delta A_6+f(x_7,y_7)\delta A_7+f(x_8,y_8)\delta A_8\\\\=f(0.5,0.5)(1)+f(1.5,0.5)(1)+f(2.5,0.5)(1)+f(3.5,0.5)(1)+f(0.5,1.5)(1)+f(1.5,1.5)(1)+f(2.5,1.5)(1)+f(3.5,1.5)(1)\\\\=0.5+0.5+1.5+0.5+2.5+0.5+3.5+0.5+0.5+1.5+1.5+1.5+2.5+1.5+3.5+1.5\\\\=24

Thus, \sum\limits^8_{i=1}f(x_i,y_i)\delta A_i=24

Evaluating the iterate integral \int\limits^4_0 \int\limits^2_0 {(x+y)} \, dydx=\int\limits^4_0 {[xy+\frac{y^2}{2} ]}\limits^2_0 \, dx =\int\limits^4_0 {[2x+2]}dx\\\\=[x^2+2x]\limits^4_0=24.

Thus, \int\limits^4_0 \int\limits^2_0 {(x+y)} \, dydx=24

You might be interested in
Can someone explain how this works and help me to find the answer?
pav-90 [236]
470 = 8.75(46 - c) + 11c
470 = 402.5 - 8.75c + 11c
67.5 = 2.25c
30 = c

If c = 30 and Soren worked 30 hours in the office, earning $11 per hour, he earns $330 from his office job. 46 - 30 = 16, which should be the remaining amount of hours Soren worked. 16 * 8.75 = 140. He earned $140 from his cashier job. $330 + $140 = $470.

The correct formula to solve this problem is A. 11c + 8.75(46 - c) = 470
8 0
3 years ago
HELP ME PLZZ asap I really need it
Furkat [3]

Answer:

20) 2/32 so colour 2 boxes

21) 7/16

22) 2/60

23) 3/8

24) 35/63 or 5/9

25) 7/32

26) 45/60 or 9/12 or 3/4

27) 1/32

28) 3/21 or 1/7

29) 13/6 × 9/2

= 117/12

30) 3/4 × 17/2

= 51/8

31) 9/8 × 10/3

= 90/24

= 45/12

= 15/4

32) 16/5 × 2/3

= 32/15

sorry if theres any calculation mistake becoz i did all the calculations in mind

Step-by-step explanation:

5 0
3 years ago
Is the following relation a function? *
spayn [35]

Answer:

No.

Step-by-step explanation:

Well at first glance it might seem so but there are two points particularly that can tell you that these points cannot be within a function.

The points (3,2) and (3,-2) will yield an undefined slope (a straight vertical line). There is no possibility that the other points can be in this line (as their y - values are different) and there is no possibilty that this is a function at all according to the vertical line test (the test is that if you draw a vertical line that there shouldn't be more than one point on it).

8 0
3 years ago
Dean had already read 1 book this year before joining a book club, and he plans to read 1 book every month now that he has joine
solniwko [45]

<em>b</em><em> </em>for <em>books</em><em> </em>read. b=1x + 1. the amount of months he's been in the club goes for x and +1 because he already read a book before he joined. if you do easy math, he's been there for 8 months because he read 9 books. i probably got the equation backwards but this works both ways imo.

6 0
3 years ago
Evaluate the following expression: -2|9|.<br> -18<br> -11<br> 11<br> 18
Blababa [14]

Answer:

-18 mat-way is good to use

6 0
3 years ago
Other questions:
  • Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit
    9·1 answer
  • Drew has 50 red,green,and blue marbles. he has six more red marbles than blue marbles and four fewer green marbles than blue mar
    8·1 answer
  • Solve this problem in your notebook using all four steps. Harvey is 3 times as old as Jane. The sum of their ages is 48 years. F
    14·1 answer
  • Help me!! Find the area of this figure.​
    9·2 answers
  • What is the reciprocal
    14·2 answers
  • 25. What is the value of x?
    15·1 answer
  • Find the measure of arc DB.
    8·1 answer
  • Please help with this
    6·2 answers
  • triumphant college is planning to increase the registration fee by 11.5%.if the registration fee is currently N$ 1000, how much
    6·1 answer
  • keri rented a canoe from a rental company for atotal of $35.00 the company charges $10.50 for the first hour and $8.25 per hour
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!