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# how do i do a definite integration

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how do i do a definite integration ex integrate y = (1/50) x^2 between 0 and 160

Jul 24, 2017

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how do i do a definite integration ex integrate y = (1/50) x^2 between 0 and 160

$$\displaystyle\int_0^{160}\;\frac{1}{50}x^2\;dx\\~\\ =\displaystyle\frac{1}{50}\int_0^{160}\;x^2\;dx\\~\\ =\displaystyle\frac{1}{50}\left[\;\frac{x^3}{3}\right]_0^{160}\\~\\ =\displaystyle\left[\;\frac{x^3}{150}\right]_0^{160}\\~\\ =\displaystyle\left[\;\frac{160^3}{150}-0\right]\\~\\ =27306\frac{2}{3}$$

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Jul 24, 2017