integration electric charges / potential
In ch 1 and 2 of class 12 physics often times integrating I find this term can anyone guide me on solving it?
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@Gyro Gearloose
Note for OP
+solved @user to close the thread when your doubt is solved. Mention the user who helped you solve the doubt. This will be added to their stats.There are formulae to integrate terms which have sqrt(a^2 + x^2), and some other forms in their deno
I have underlined the formula you will need to use for solving this integral.
You can read from page 243 onwards to find the derivation of these results.
https://ncert.nic.in/textbook.php?lemh2=1-7
I am talking about where they assumed the term to be 't' or take to tan0 I did not understand that
Taking $r^2 + x^2 = t^2$
we have
$2rdr = 2tdt$
or, $rdr=tdt$
so the integral becomes:
$\int \frac{tdt}{t^3}$
or, $\int \frac{dt}{t^2}
or, $$\frac{-1}{t}$$
or, $$\frac{-1}{\sqrt{r^2 + x^2}}$$
Keshav
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Oh okay.
Let x= atan(theta). Then we are going to use substitution method. So dx = a sec^2(theta) d(theta)
in deno you will replace x^2 with a^2 tan^2(theta)
You meant this way right? Please correct me if I was wrong
yes this but insted of dx it was x dx , i did not wanted to know it for a specific term rather i wanted to know the logic behind it so if the terms are twisted i can still do it
yes i was looking for this
+solved @Keshav
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