_0^3 , ( 1 x^2 , , + , ,4 ,x , , + , ,4 , , , + , , , x^2 , , - ,… - Vidyadip

MCQ

$\int\limits_0^3 \, \left( {\frac{1}{{\sqrt {{x^2}\,\, + \,\,4\,x\,\, + \,\,4} }}\,\,\, + \,\,\,\sqrt {{x^2}\,\, - \,\,4\,x\,\, + \,\,4} \,} \right)\, dx =$

A
ln $\frac{5}{2}\,\, - \,\,\frac{3}{2}$
B
ln $\frac{5}{2}\,\, + \,\,\frac{3}{2}$
✓
ln $\frac{5}{2}\,\, + \,\,\frac{5}{2}$
D
none

✓

Answer

Correct option: C.

ln $\frac{5}{2}\,\, + \,\,\frac{5}{2}$

c
$I = \int\limits_0^3 {(\frac{1}{{|x + 2|}} + |x - 2|\,)\,dx} $ $= \int\limits_0^3 {\frac{{dx}}{{x + 2}}\,dx} $ $+ \int\limits_0^3 {|x + 2|\,dx} $

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