- #1
GreenPrint
- 1,196
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Hi,
I was wondering if it was really necessary to evaluate improper integrals with limits? Could anyone really say I was wrong if I did something like
find the area bounded by the region y=1/x^2, x=2, and the x-axis
integral[1,inf] dx/x^2 = (-1/x)|[2,inf] = (-0)-(-1/2)=1/2
Like I don't really see the need to remove infinity from my work and plug in some variable and evaluate using limits when I can just plug in infinity if that makes sense and was wondering if anyone would consider my work to be wrong because my textbook insists that I evaluate improper integrals with limits but I see no real reason to
also if there was a problem were limits were necessary and I would get a undefined answer I evaluate improper integrals with like 3^+ or 3^- to indicate I was evaluating the integral from the right of 3 or to the left of 3
I was wondering if it was really necessary to evaluate improper integrals with limits? Could anyone really say I was wrong if I did something like
find the area bounded by the region y=1/x^2, x=2, and the x-axis
integral[1,inf] dx/x^2 = (-1/x)|[2,inf] = (-0)-(-1/2)=1/2
Like I don't really see the need to remove infinity from my work and plug in some variable and evaluate using limits when I can just plug in infinity if that makes sense and was wondering if anyone would consider my work to be wrong because my textbook insists that I evaluate improper integrals with limits but I see no real reason to
also if there was a problem were limits were necessary and I would get a undefined answer I evaluate improper integrals with like 3^+ or 3^- to indicate I was evaluating the integral from the right of 3 or to the left of 3
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