Finding new limits of integration problem

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SUMMARY

The discussion focuses on evaluating improper integrals, specifically the integral of e^(-sqrt(x)) / sqrt(x) from 1 to infinity and the integral of x^2/(1+x^3) from 0 to infinity. The first integral is transformed using the substitution u = -sqrt(x), leading to a change in bounds and a multiplication by -1. The second integral involves the substitution u = 1 + x^3, where the bounds remain unchanged, and the user inquires about the necessity of switching bounds and multiplying by -1 in this context. The consensus is that the rules of integration must be applied consistently, regardless of the specific problem.

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coolguy1
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In the integral

integral(1,infinity) e^(-sqrt(x)) / sqrt(x)

STEP 1:
I let u = -sqrt(x)
du = -1/(2sqrt(x))

then my lower bound u = -1
then my upper bound u = -infinity

-2 integral(-1,infinity) e^u du

I would then switch the order of the integration bounds and multiply by -1My question is in the next problem integral(0,infinity) x^2/(1+x^3) dx
I let u = 1 + x^3
du = 3x^2 dx
du/3 = x^2 dx

lower bound u = 1
upper bound u = infinity

My question is: Would you multiply by -1 and switch the lower and upper bounds in this problem, or was that just the case in the previous problem?Thanks for your help and sorry I'm new to the commands and not sure how to use them yet.
 
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In fact, it doesn't matter as long as you apply the rules correctly.
 

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