Sketch the region bounded by the graphs of the given equations and find the area of their region.

y=\frac{x}{x^{2}+5}

y=-\frac{1}{6} x^{2}

x=1

A) $Sketch the region bounded by the graphs of the given equations and find the area of their region. y=\frac{x}{x^{2}+5} , y=-\frac{1}{6} x^{2} , x=1 A) \ln \left(\frac{6}{5}\right) B) 4-\ln \left(\frac{6}{5}\right) C) \frac{1}{2} \ln \left(\frac{6}{5}\right)+\frac{1}{18} D) \frac{1}{2} \ln \left(\frac{6}{5}\right)-\frac{1}{18}$

\ln \left(\frac{6}{5}\right)

B) $Sketch the region bounded by the graphs of the given equations and find the area of their region. y=\frac{x}{x^{2}+5} , y=-\frac{1}{6} x^{2} , x=1 A) \ln \left(\frac{6}{5}\right) B) 4-\ln \left(\frac{6}{5}\right) C) \frac{1}{2} \ln \left(\frac{6}{5}\right)+\frac{1}{18} D) \frac{1}{2} \ln \left(\frac{6}{5}\right)-\frac{1}{18}$

4-\ln \left(\frac{6}{5}\right)

C) $Sketch the region bounded by the graphs of the given equations and find the area of their region. y=\frac{x}{x^{2}+5} , y=-\frac{1}{6} x^{2} , x=1 A) \ln \left(\frac{6}{5}\right) B) 4-\ln \left(\frac{6}{5}\right) C) \frac{1}{2} \ln \left(\frac{6}{5}\right)+\frac{1}{18} D) \frac{1}{2} \ln \left(\frac{6}{5}\right)-\frac{1}{18}$

\frac{1}{2} \ln \left(\frac{6}{5}\right)+\frac{1}{18}

D) $Sketch the region bounded by the graphs of the given equations and find the area of their region. y=\frac{x}{x^{2}+5} , y=-\frac{1}{6} x^{2} , x=1 A) \ln \left(\frac{6}{5}\right) B) 4-\ln \left(\frac{6}{5}\right) C) \frac{1}{2} \ln \left(\frac{6}{5}\right)+\frac{1}{18} D) \frac{1}{2} \ln \left(\frac{6}{5}\right)-\frac{1}{18}$

\frac{1}{2} \ln \left(\frac{6}{5}\right)-\frac{1}{18}

Use the Method of Cylindrical Shells to Find the Volume y=1x(x2+144)y=\frac{1}{x\left(x^{2}+144\right)}y=x(x2+144)1​

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Use the Method of Cylindrical Shells to Find the Volume $y=\frac{1}{x\left(x^{2}+144\right)}$

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