Question

three cubes of side 4cm each are placed one above another.The volume of the resulting cuboid will be?​

Answer 1

$\huge\mathcal{\mid{\mid{\underline{\pink{Good\: Afternoon\:}}}{\mid{\mid}}}}$

$\Large{\colorbox{pink}{\bf{\green{QuEsTiOn;-}}}}$

$\red\checkmark\:\:\bf\blue{Integral\:of\:\dfrac{\sqrt{tanx}}{sinx.cosx}}$

$\huge{\orange{\boxed{\fcolorbox{lime}{indigo}{\color{aqua}ANSWER}}}}$

$:\implies\:\:\Large\bf{\int\:\dfrac{\sqrt{tanx}}{sinx.cosx}\:dx}$

$:\implies\:\:\bf{\int\:\dfrac{\sqrt{tanx}}{(\frac{sinx.cosx}{cos^2x})\:cos^2x}\:dx}$

$:\implies\:\:\bf{\int\:\dfrac{\sqrt{tanx}}{(\frac{sinx}{cosx})\:cos^2x}\:dx}$

$:\implies\:\:\bf{\int\:\dfrac{\sqrt{tanx}}{tanx}\:.\:sec^2x\:dx}$

$:\implies\:\:\bf{\int\:\dfrac{1}{\sqrt{tanx}}\:.\:sec^2x\:dx}$

$\Large\bf\pink{Let}$

$\bf{tanx\:=\:t}$

$\longmapsto\:\:\bf{sec^2x\:.\:dx\:=\:dt\:}$

$:\implies\:\:\bf{\int\:\dfrac{1}{t^{1/2}}\:.\:dt}$

$:\implies\:\:\bf{\int\:t^{-\:\frac{1}{2}}\:.\:dt}$

$:\implies\:\:\bf{\dfrac{t^{-\:\frac{1}{2}\:+\:1}}{-\:\frac{1}{2}\:+\:1}\:+\:c}$

$:\implies\:\:\bf{\dfrac{t^{\frac{1}{2}}}{\frac{1}{2}}\:+\:c}$

$:\implies\:\:\bf{2\:t^{\frac{1}{2}}\:+\:c}$

$:\implies\:\:\bf\green{2\:\sqrt{tanx}\:+\:c}$