Mathematics

# $x_{CM} = \frac{\int x dm}{\int dm} = \frac{\int\limits_0^1 x (1 + 2x) dx}{\int\limits_0^1(1 + 2x) dx}$

##### SOLUTION
$\int^1_0 x (1+2x)dx$ $= \int^1_0(x+2x^2)dx \\ =(\dfrac{x^2}{2}+\dfrac{2x^2}{3})\bigg|^1_0 \ \\ =\dfrac{1}{2}+\dfrac{2}{3} = \dfrac{7}{6}$
$\int^1_0 (1+2x)dx$ $\\ =(x+x^2)\bigg|^1_0 \ \\ =1+1 = 2$
$x_{CM} = \dfrac{\int^1_0 x(1+2x)dx}{\int^1_0 (1+2x)dx}$
$\implies \ x_{CM} = \dfrac{7}{12}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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