Mathematics Exam > Mathematics Questions > Which one of the following is/are correct?a)i...
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Which one of the following is/are correct?
- a)if
for every point of E, then (fdx + gdy) is an exact. - b)if
for every point of E and if A and B are any two points of E then the line integral 
has the same value for every path from A to B, provided the path lies in E - c)If the line integral
is independent of the path from A to B, where A and B are any two points of E and the path AB lies in E then 
for every point (x,y) of E - d)Area of the region E which is bounded by contour E, with respect to both the axes is
Correct answer is option 'A,B,C,D'. Can you explain this answer?
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Which one of the following is/are correct?a)iffor every point of E, th...
Option - (A) It is already clear that if 
for every point of E, then (fdx + gdy)
for every point of E, then (fdx + gdy) is an exact differential.
Option-(B) Let ACB and ADB be any two curves joining A and B, that lies inE and do not meet each other at any point other than A and B. green's th. holds for the region E' bounded by the curve ACBDA , but the double integral over E ' = 0 because
at every paint in E' and therefore the line integral along the bounding curve ACBDA is Zero,
both integrals are equal.
Option - C Let E' C E be a region enclosed by curve ACBDA which lies i'n E,
If the continuous fn (gx- fy) is not ze ro at an arbitrary point P of E, thee is a region E' surrounding P in which (gn- fy) has the same sign as at P and the integration over ACBDA could not be Zero, which is a contradiction. Hence gn - fy = 0 or gx = fy, at every paint of E.
Option -D If f(x,y) = y. Then area of a domain which is piecewise regular with respect to y-axis,
Similarly putting g(x,4) -x, we see that the area of a domain, piecewise regular with respect to x-axis,
putting g(x,y) = x and f(x,y) = - y then
Most Upvoted Answer
Which one of the following is/are correct?a)iffor every point of E, th...
Option - (A) It is already clear that if for every point of E, then (fdx + gdy)
for every point of E, then (fdx + gdy) is an exact differential.
Option-(B) Let ACB and ADB be any two curves joining A and B, that lies inE and do not meet each other at any point other than A and B. green's th. holds for the region E' bounded by the curve ACBDA , but the double integral over E ' = 0 because
at every paint in E' and therefore the line integral along the bounding curve ACBDA is Zero,both integrals are equal.
Option - C Let E' C E be a region enclosed by curve ACBDA which lies i'n E,
If the continuous fn (gx- fy) is not ze ro at an arbitrary point P of E, thee is a region E' surrounding P in which (gn- fy) has the same sign as at P and the integration over ACBDA could not be Zero, which is a contradiction. Hence gn - fy = 0 or gx = fy, at every paint of E.
Option -D If f(x,y) = y. Then area of a domain which is piecewise regular with respect to y-axis,
Similarly putting g(x,4) -x, we see that the area of a domain, piecewise regular with respect to x-axis,
putting g(x,y) = x and f(x,y) = - y then
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Which one of the following is/are correct?a)iffor every point of E, then (fdx + gdy) is an exact.b)iffor every point of E and if A and B are any two points of E then the line integralhas the same value for every path from A to B, provided the path lies in Ec)If the line integralis independent of the path from A to B, where A and B are any two points of E and the path AB lies in E thenfor every point (x,y) of Ed)Area of the region E which is bounded by contour E, with respect to both the axes isCorrect answer is option 'A,B,C,D'. Can you explain this answer?
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Which one of the following is/are correct?a)iffor every point of E, then (fdx + gdy) is an exact.b)iffor every point of E and if A and B are any two points of E then the line integralhas the same value for every path from A to B, provided the path lies in Ec)If the line integralis independent of the path from A to B, where A and B are any two points of E and the path AB lies in E thenfor every point (x,y) of Ed)Area of the region E which is bounded by contour E, with respect to both the axes isCorrect answer is option 'A,B,C,D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which one of the following is/are correct?a)iffor every point of E, then (fdx + gdy) is an exact.b)iffor every point of E and if A and B are any two points of E then the line integralhas the same value for every path from A to B, provided the path lies in Ec)If the line integralis independent of the path from A to B, where A and B are any two points of E and the path AB lies in E thenfor every point (x,y) of Ed)Area of the region E which is bounded by contour E, with respect to both the axes isCorrect answer is option 'A,B,C,D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is/are correct?a)iffor every point of E, then (fdx + gdy) is an exact.b)iffor every point of E and if A and B are any two points of E then the line integralhas the same value for every path from A to B, provided the path lies in Ec)If the line integralis independent of the path from A to B, where A and B are any two points of E and the path AB lies in E thenfor every point (x,y) of Ed)Area of the region E which is bounded by contour E, with respect to both the axes isCorrect answer is option 'A,B,C,D'. Can you explain this answer?.
Which one of the following is/are correct?a)iffor every point of E, then (fdx + gdy) is an exact.b)iffor every point of E and if A and B are any two points of E then the line integralhas the same value for every path from A to B, provided the path lies in Ec)If the line integralis independent of the path from A to B, where A and B are any two points of E and the path AB lies in E thenfor every point (x,y) of Ed)Area of the region E which is bounded by contour E, with respect to both the axes isCorrect answer is option 'A,B,C,D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which one of the following is/are correct?a)iffor every point of E, then (fdx + gdy) is an exact.b)iffor every point of E and if A and B are any two points of E then the line integralhas the same value for every path from A to B, provided the path lies in Ec)If the line integralis independent of the path from A to B, where A and B are any two points of E and the path AB lies in E thenfor every point (x,y) of Ed)Area of the region E which is bounded by contour E, with respect to both the axes isCorrect answer is option 'A,B,C,D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is/are correct?a)iffor every point of E, then (fdx + gdy) is an exact.b)iffor every point of E and if A and B are any two points of E then the line integralhas the same value for every path from A to B, provided the path lies in Ec)If the line integralis independent of the path from A to B, where A and B are any two points of E and the path AB lies in E thenfor every point (x,y) of Ed)Area of the region E which is bounded by contour E, with respect to both the axes isCorrect answer is option 'A,B,C,D'. Can you explain this answer?.
Solutions for Which one of the following is/are correct?a)iffor every point of E, then (fdx + gdy) is an exact.b)iffor every point of E and if A and B are any two points of E then the line integralhas the same value for every path from A to B, provided the path lies in Ec)If the line integralis independent of the path from A to B, where A and B are any two points of E and the path AB lies in E thenfor every point (x,y) of Ed)Area of the region E which is bounded by contour E, with respect to both the axes isCorrect answer is option 'A,B,C,D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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Which one of the following is/are correct?a)iffor every point of E, then (fdx + gdy) is an exact.b)iffor every point of E and if A and B are any two points of E then the line integralhas the same value for every path from A to B, provided the path lies in Ec)If the line integralis independent of the path from A to B, where A and B are any two points of E and the path AB lies in E thenfor every point (x,y) of Ed)Area of the region E which is bounded by contour E, with respect to both the axes isCorrect answer is option 'A,B,C,D'. Can you explain this answer?, a detailed solution for Which one of the following is/are correct?a)iffor every point of E, then (fdx + gdy) is an exact.b)iffor every point of E and if A and B are any two points of E then the line integralhas the same value for every path from A to B, provided the path lies in Ec)If the line integralis independent of the path from A to B, where A and B are any two points of E and the path AB lies in E thenfor every point (x,y) of Ed)Area of the region E which is bounded by contour E, with respect to both the axes isCorrect answer is option 'A,B,C,D'. Can you explain this answer? has been provided alongside types of Which one of the following is/are correct?a)iffor every point of E, then (fdx + gdy) is an exact.b)iffor every point of E and if A and B are any two points of E then the line integralhas the same value for every path from A to B, provided the path lies in Ec)If the line integralis independent of the path from A to B, where A and B are any two points of E and the path AB lies in E thenfor every point (x,y) of Ed)Area of the region E which is bounded by contour E, with respect to both the axes isCorrect answer is option 'A,B,C,D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which one of the following is/are correct?a)iffor every point of E, then (fdx + gdy) is an exact.b)iffor every point of E and if A and B are any two points of E then the line integralhas the same value for every path from A to B, provided the path lies in Ec)If the line integralis independent of the path from A to B, where A and B are any two points of E and the path AB lies in E thenfor every point (x,y) of Ed)Area of the region E which is bounded by contour E, with respect to both the axes isCorrect answer is option 'A,B,C,D'. Can you explain this answer? tests, examples and also practice Mathematics tests.
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