- #1
marellasunny
- 255
- 3
[tex]
\int_0^1 \frac{1}{\sqrt{x}}\,\mathrm{d}x
[/tex]
=
[tex]
\lim_{\varepsilon \to 0+}\int_\varepsilon^1 \frac{1}{\sqrt{x}}\,\mathrm{d}x
[/tex]
My question is about the usage of 0+ in the limit.(I evaluated the integrals and arrived at the part where I substitute upper and lower limits.)
Did the author deliberately choose to use [tex]\lim_{\varepsilon \to 0+} [/tex] instead of 0 or 0- so that any imaginary numbers arising from the expression [tex]2\sqrt{x}[/tex] do not arise?
Or is there any other reason?
Thanks.
\int_0^1 \frac{1}{\sqrt{x}}\,\mathrm{d}x
[/tex]
=
[tex]
\lim_{\varepsilon \to 0+}\int_\varepsilon^1 \frac{1}{\sqrt{x}}\,\mathrm{d}x
[/tex]
My question is about the usage of 0+ in the limit.(I evaluated the integrals and arrived at the part where I substitute upper and lower limits.)
Did the author deliberately choose to use [tex]\lim_{\varepsilon \to 0+} [/tex] instead of 0 or 0- so that any imaginary numbers arising from the expression [tex]2\sqrt{x}[/tex] do not arise?
Or is there any other reason?
Thanks.