I was trying to solve simple integration problem, integration x from 0-infinite. Is there any particular answer to the question from any other methods? My try is I've shown on picture below.
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Ѕᴀᴀᴅ
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Surya Bhusal
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1You forgot to change limits when you substituted z. Further as x approaches infinite, the integral also approaches infinite – Anvit Mar 03 '18 at 03:31
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1mathjax reference to help you type maths directly on the site. – Siong Thye Goh Mar 03 '18 at 03:36
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@downvoters The question has been significantly improved, an attempt has been given. – Sarvesh Ravichandran Iyer Mar 03 '18 at 03:47
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I don't think it's needed to type all those equation because what matters is i am here to learn. I find it's easy to type on Microsoft Word platform rather typing whole equation, which makes a lot more easier. – Surya Bhusal Mar 03 '18 at 04:34
2 Answers
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Your mistake: As you change your variable to $z$, the variable is not change back.
Remark: Rather than $90$, you might want to work with radian.
$$\lim_{M \to \infty} \int_0^M x \, dx= \lim_{M \to \infty}\frac{M^2}2 = \infty$$
Siong Thye Goh
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I would re-interpret problem to be for $0<a$, what is the limit as $a$ goes to infinity of $\int_0^a xdx.$ When $0<a$, $\int_0^a xdx = \displaystyle\frac{a^2}{2}.$ Therefore, the (re-interpreted) problem is equivalent to asking: what is the limit as $a$ goes to infinity of $\displaystyle\frac{a^2}{2}.$ Obviously, as $a$ goes to infinity, $\displaystyle\frac{a^2}{2}$ goes to infinity.
This approach is very similar to Siong Thye Goh's approach, except that I scrap the whole polar coordinates / radians approach and just stay with the algebra.
user2661923
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