Mumbai University > First Year Engineering > sem 2 > Applied Maths 2

Marks : 3

Year : 2015

Let $x=2t$ when $x \to 2\space \space t=1$

When $x=0 , t=0$

$dx=2dt$

$I=\int\limits_0^1(2t)^2(2-2t)^3 2 dt$

$I=8\int\limits_0^1t^22^3(1-t)^3 dt$

$I=64\int\limits_0^1t^2(1-t)^3 dt$

$I=64\beta(3,4)$

$I=\dfrac {64\times2!\times 3!}{6!}$

$=\dfrac {64\times2!\times 3!}{6\times5\times4\times3!}$

$=\dfrac {31}{30}$