91Ó°ÊÓ

Find the average value of the function on the given interval. $$ f(x)=4 x-x^{2}, \quad[0,4] $$

How much work is done in lifting a \(40-\mathrm{kg}\) sandbag to a height of 1.5 \(\mathrm{m} ?\)

\(1 - 18\) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. $$ y = 2 - \frac { 1 } { 2 } x , y = 0 , x = 1 , x = 2 ; \quad \text { about the } x $$

\(1 - 18\) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. $$ y = 1 - x ^ { 2 } , y = 0 ; \quad \text { about the } x $$

Find the average value of the function on the given interval. $$ f(x)=\sin 4 x, \quad[-\pi, \pi] $$

Find the work done if a constant force of 100 \(\mathrm{lb}\) is used to pull a cart a distance of 200 \(\mathrm{ft} .\)

A particle is moved along the \(x\) -axis by a force that measures 10\(/(1+x)^{2}\) pounds at a point \(x\) feet from the origin. Find the work done in moving the particle from the origin to a distance of 9 \(\mathrm{ft.}\)

\(3-7\) Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the \(y\) -axis. Sketch the region and a typical shell. $$ y=1 / x, \quad y=0, \quad x=1, \quad x=2 $$

Find the average value of the function on the given interval. $$ g(x)=\sqrt[3]{x}, \quad[1,8] $$

\(3-7\) Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the \(y\) -axis. Sketch the region and a typical shell. $$y=x^{2}, \quad y=0, \quad x=1$$