Question

Integration of integral with upper and lower limit as q2 and q1 of funtion -Kq1q2/x^2
dx

Answer 1

Answer:

$\sf \displaystyle I = K \ \left[q2-q1\right]$

Explanation:

We are ask to integrate the following :

$\sf \displaystyle I = \int\limits^{q2}_{q1} {\dfrac{K \ q1 \ q2}{x^2} } \, dx$

$\sf \displaystyle I =K \ q1 \ q2 \int\limits^{q2}_{q1} {x^{-2} } \, dx$

$\sf \displaystyle I =K \ q1 \ q2 \left|\dfrac{x^{-2+1}}{-2+1}\right|^{q2}_{q1}$

$\sf \displaystyle I =K \ q1 \ q2 \left|\dfrac{x^{-1}}{-1}\right|^{q2}_{q1}$

$\sf \displaystyle I =-K \ q1 \ q2 \left|\dfrac{1}{x}\right|^{q2}_{q1}$

$\sf \displaystyle I =- K \ q1 \ q2 \left[\dfrac{1}{q2}- \dfrac{1}{q1} \right]$

$\sf \displaystyle I =-K \ q1 \ q2 \left[\dfrac{q1-q2}{q1 \ q2}\right]$

$\sf \displaystyle I =-K \ \left[\dfrac{q1-q2}{1}\right]$

$\sf \displaystyle I = K \ \left[q2-q1\right]$

Hence we get answer.