Mathematics Exam > Mathematics Questions > Int(int[x+y]*dx*dy, where limite=R, over the ...
Start Learning for Free
Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'?
Most Upvoted Answer
Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], ...
Calculation of the Integral
- To calculate the integral of int(int[x+y]*dx*dy) over the rectangle R=[0,1]*[0,2], we first need to understand the function int[x+y].
Understanding the Greatest Integer Function
- The greatest integer function, int[x], also known as the floor function, gives the largest integer less than or equal to x. For example, int[3.7] = 3, int[5.2] = 5, and int[-2.3] = -3.
Representation of int[x+y]
- In this case, the function int[x+y] represents the greatest integer less than or equal to the sum of x and y.
Integration over the Rectangle R
- The rectangle R=[0,1]*[0,2] is a 1x2 rectangle with the x-coordinate ranging from 0 to 1 and the y-coordinate ranging from 0 to 2.
Calculating the Integral
- To calculate the double integral of int[x+y] over the rectangle R, we need to evaluate the integral with respect to x and y.
- The integral can be written as int(int[int[x+y]*dx]dy) over the limits [0,1] for x and [0,2] for y.
- By evaluating the integral with the given limits, we can find the result of the double integral over the rectangle R.
By following these steps and understanding the concepts involved, you can successfully calculate the integral of int[x+y] over the rectangle R=[0,1]*[0,2].
- To calculate the integral of int(int[x+y]*dx*dy) over the rectangle R=[0,1]*[0,2], we first need to understand the function int[x+y].
Understanding the Greatest Integer Function
- The greatest integer function, int[x], also known as the floor function, gives the largest integer less than or equal to x. For example, int[3.7] = 3, int[5.2] = 5, and int[-2.3] = -3.
Representation of int[x+y]
- In this case, the function int[x+y] represents the greatest integer less than or equal to the sum of x and y.
Integration over the Rectangle R
- The rectangle R=[0,1]*[0,2] is a 1x2 rectangle with the x-coordinate ranging from 0 to 1 and the y-coordinate ranging from 0 to 2.
Calculating the Integral
- To calculate the double integral of int[x+y] over the rectangle R, we need to evaluate the integral with respect to x and y.
- The integral can be written as int(int[int[x+y]*dx]dy) over the limits [0,1] for x and [0,2] for y.
- By evaluating the integral with the given limits, we can find the result of the double integral over the rectangle R.
By following these steps and understanding the concepts involved, you can successfully calculate the integral of int[x+y] over the rectangle R=[0,1]*[0,2].
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'?
Question Description
Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'?.
Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'?.
Solutions for Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'? defined & explained in the simplest way possible. Besides giving the explanation of
Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'?, a detailed solution for Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'? has been provided alongside types of Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'? theory, EduRev gives you an
ample number of questions to practice Int(int[x+y]*dx*dy, where limite=R, over the rectangle R=[0,1]*[0,2], where [x] is greatest integer function of 'x'? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup