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Math Help - Improper Integral: Volume Around x-axis

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    Question Improper Integral: Volume Around x-axis

    let f(x)=1/(0.5x+1.8), by rotating R={(x,y)/ x>=0,0<=y<=1/(0.5x+1.8)}about the x axis we obtain a solid , Calculate the volume
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    Quote Originally Posted by shannon1111 View Post
    let f(x)=1/(0.5x+1.8), by rotating R={(x,y)/ x>=0,0<=y<=1/(0.5x+1.8)}about the x axis we obtain a solid , Calculate the volume
    f(x) = \frac{2}{x+3.6}

    V = \pi \int_0^{\infty} \left(\frac{2}{x+3.6}\right)^2 \, dx

    V = 4\pi \lim_{b \to \infty} \int_0^b \frac{1}{(x+3.6)^2} \, dx

    V = 4\pi \lim_{b \to \infty} \left[-\frac{1}{x+3.6}\right]_0^b

    V = 4\pi \lim_{b \to \infty} \left[\frac{1}{3.6}-\frac{1}{b+3.6}\right] = \frac{10\pi}{9}
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