Question

${\int }_4^{10}\frac{\left[x^2\right]dx}{[x^2-28x+196]+\left[x^2\right]}$=

Answer 1

$I={\int }_4^{10}$ $\frac{\left[x^2\right]dx}{\left[\right(x-14{)}^2]+\left[x^2\right]}$.....(i)

applying $a+b-x$ property $\Rightarrow$

$I={\int }_4^{10}\frac{\left[\right(x-14{)}^2]dx}{\left[x^2\right]+\left[\right(x-14{)}^2]}$.....(ii)

$\left(i\right)+\left(ii\right)\Rightarrow$

$2I={\int }_4^{10}dx$

$2I=6$

$I=3$