Mathematics, 21.11.2019 18:31 jayyla32
Find the area under the curve y = 25/x3 from x = 1 to x = t. evaluate the area under the curve for t = 10, t = 100, and t = 1000. t = 10 t = 100 t = 1000 find the total area under this curve for x ≥ 1.
Answers: 2
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from x = 1 to x = t, is to calculate the next integral ![\int_{1}^{t}\frac{25}{x^3} dx = \int_{1}^{t} 25x^{-3} dx = 25\frac{x^{-2}}{-2}|_{1}^{t} = (-25/2)x^{-2}|_{1}^{t} = (-25/2)[t^{-2}-1]](/tpl/images/0384/8268/5edc0.png)
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![(-25/2)[\frac{1}{10^2}-1] = 12.375](/tpl/images/0384/8268/e25dd.png)
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![(-25/2)[\frac{1}{100^2}-1] = 12.49875](/tpl/images/0384/8268/feb59.png)
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![(-25/2)[\frac{1}{1000^2}-1] = 12.49999](/tpl/images/0384/8268/1a748.png)
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is given by
![lim_{t\to\infty}(-25/2)[t^{-2}-1] = (-25/2)(-1) = 25/2 = 12.5](/tpl/images/0384/8268/2c687.png)
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Find the area under the curve y = 25/x3 from x = 1 to x = t. evaluate the area under the curve for t...
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