Quick Integration Question: order of integration limits

G

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When you're evaluating an integral say... something from 10 to 2 ( when the number on bottom is larger than the one on top) how does that change the evaluation of the integral? Thanks.
 
It just means that you subtract (at the end) "backwards". In other words, you'll get the same value, but with the opposite sign.

Eliz.
 
Note: This fact can be used to create otherwise unsolveable exercises (especially on tests).

For instance, you might be given that int[a,b][f(x)]dx = A and that int[c,a][f(x)]dx = B; then you might be asked to find int[b,c][f(x)]dx. They wouldn't give you f(x), nor any values for a, b, or c. But you can answer the question:

. . . . .int[b,c][f(x)]dx

. . . . .= int[a,c][f(x)]dx - int[a,b][f(x)]dx

. . . . .= -int[c,a][f(x)]dx - int[a,b][f(x)]dx

. . . . .= -B - A

And this symbolic answer would be what they were looking for.

Just FYI... :wink:

Eliz.
 
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