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
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