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junior college 2 | H2 Maths
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for the definite integral, why is it ‘0’ at the top and ‘1/4’ at the bottom? isn’t it suppose to be the other way round since the greater value is written at the top (0> 1/4)
Date Posted: 4 years ago
Views: 303
Integrals do not always have to be a larger number on top and a smaller number below. Integrals do exist the other way as well!
In this case, after the substitution, the integral does become 0 and 1/4; however, this is correct as the substitutions come naturally from the previous results. Here a change is a bad idea.
Take the simplest case
y = 9 - x
And we integrate from 0 to 9.
We should get the solution as 40.5, since this is a triangle of 9 by 9.
What if we had used u = 9 - x instead? Well, the upper limit becomes 0 while the lower limit becomes 9. Then, du = -dx and thus dx = -du.
The expression becomes y = -u du. The limits remain 0 on top and 9 below. You will see that this integrates to 40.5. Had you swapped the values, you would have obtained negative 40.5.
In this case, after the substitution, the integral does become 0 and 1/4; however, this is correct as the substitutions come naturally from the previous results. Here a change is a bad idea.
Take the simplest case
y = 9 - x
And we integrate from 0 to 9.
We should get the solution as 40.5, since this is a triangle of 9 by 9.
What if we had used u = 9 - x instead? Well, the upper limit becomes 0 while the lower limit becomes 9. Then, du = -dx and thus dx = -du.
The expression becomes y = -u du. The limits remain 0 on top and 9 below. You will see that this integrates to 40.5. Had you swapped the values, you would have obtained negative 40.5.
thank you!!!
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Hello! It is because you are changing from dy to dx so you have to change the limits too!
When dy,
Ur top limit is ‘1/2’ right so when you change it to dx form it becomes ‘0’ like what your notes says in the box change the limit. Same for the the bottom integral! So its not always greater value on top, you follow the previous limit when it was in dy form :)
When dy,
Ur top limit is ‘1/2’ right so when you change it to dx form it becomes ‘0’ like what your notes says in the box change the limit. Same for the the bottom integral! So its not always greater value on top, you follow the previous limit when it was in dy form :)
Date Posted:
4 years ago
thank you!!! :)
thank u:)
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