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imagreencat
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We were to asked to get the integral from 0 to infinity of (dx)/(sqrt(x))(x+1). I don't know if I should use the infinite intervals AND the discontinuous integrand or should I just go with one?
 2 years ago
 2 years ago
imagreencat Group Title
We were to asked to get the integral from 0 to infinity of (dx)/(sqrt(x))(x+1). I don't know if I should use the infinite intervals AND the discontinuous integrand or should I just go with one?
 2 years ago
 2 years ago

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lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
split them up first
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
1 to infity and 0 to 1 should work
 2 years ago

imagreencat Group TitleBest ResponseYou've already chosen the best response.0
So I would split them up first, then use an infinite interval from 1 to infinity and the discontinuous integrand from 0 to 1? :)
 2 years ago

imagreencat Group TitleBest ResponseYou've already chosen the best response.0
Okay. Thanks so much for the help!!
 2 years ago

PaxPolaris Group TitleBest ResponseYou've already chosen the best response.0
\[\large \int\limits_{0}^{\infty}{dx \over \sqrt {x} \left( x+1 \right)}\]??
 2 years ago

PaxPolaris Group TitleBest ResponseYou've already chosen the best response.0
substitute \(\large \sqrt x = u\) and \(\large du =\Large \frac 12 \cdot\frac 1 {\sqrt x}\) \[\Large = 2\int\limits_0^\infty {1 \over u^2+1}du \] \[\Large = \left[ 2\tan^{1}(u) \right]_0^\infty=2 \cdot \frac \pi 20 = \Huge\pi\]
 2 years ago
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