Find the volume generated by revolving the area bounded by \begin{equation} y = \frac{1}{x^3 + 5x^2 + 4x}, \quad x = 7, x = 17 \text{ and } y = 0 \end{equation} around the $y$-axis. \begin{equation} V = \end{equation} help (numbers)

          Find the volume generated by revolving the area bounded by \begin{equation*} y = \frac{1}{x^3 + 5x^2 + 4x}, \quad x = 7, x = 17 \text{ and } y = 0 \end{equation*} around the $y$-axis. \begin{equation*} V = \end{equation*} help (numbers)

Find the volume generated by revolving the area bounded by
y = (1)/(x^3 + 5x^2 + 4x), x = 7, x = 17 and y = 0
around the y-axis.
V =
help (numbers)

Added by Jacqueline M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

07/21/2022

Step 1

To find the points of intersection, set y=0 and solve for x: 0 = 1/(x^(3)+5x^(2)+4x) 0 = 1/x(x^2 + 5x + 4) 0 = 1/x(x+1)(x+4) This gives x=0, x=-1, and x=-4 as the x-values where y=0. However, since x=0 is not within the bounds of x=7 and x=17, we only consider Show more…

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Find the volume generated by revolving the area bounded by y=(1)/(x^(3)+5x^(2)+4x),x=7,x=17 and y=0 around the y-axis. V= help (numbers) Find the volume generated by revolving the area bounded by 1 V. help (numbers)