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Evaluate the $\int\limits_0^2x^2(2-x)^3dx$
written 7.8 years ago by | modified 2.2 years ago by |
Mumbai University > First Year Engineering > sem 2 > Applied Maths 2
Marks : 3
Year : 2015
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written 7.8 years ago by | modified 2.2 years ago by |
Mumbai University > First Year Engineering > sem 2 > Applied Maths 2
Marks : 3
Year : 2015
written 7.8 years ago by |
Let $x=2t$ when $x \to 2\space \space t=1$
When $x=0 , t=0$
$dx=2dt$
$I=\int\limits_0^1(2t)^2(2-2t)^3 2 dt$
$I=8\int\limits_0^1t^22^3(1-t)^3 dt$
$I=64\int\limits_0^1t^2(1-t)^3 dt$
$I=64\beta(3,4)$
$I=\dfrac {64\times2!\times 3!}{6!}$
$=\dfrac {64\times2!\times 3!}{6\times5\times4\times3!}$
$=\dfrac {31}{30}$