Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Problem 8
A spring has a natural length of \(40 \mathrm{cm} .\) If a \(60-\mathrm{N}\) force is required to keep the spring compressed \(10 \mathrm{cm},\) how much work is done during this compression? How much work is required to compress the spring to a length of \(25 \mathrm{cm} ?\)
Problem 8
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. $$ y=6-x^{2}, y=2 ; \text { about the } x \text { -axis } $$
Problem 9
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. $$ y^{2}=x, x=2 y ; \text { about the } y \text { -axis } $$
Problem 9
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to \(x\) or \(y .\) Draw a typical approximating rectangle and label its height and width. Then find the area of the region. $$ y=1 / x, \quad y=1 / x^{2}, \quad x=2 $$
Problem 9
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the \(x\) -axis. $$ x y=1, \quad x=0, \quad y=1, \quad y=3 $$
Problem 9
(a) Find the average value of \(f\) on the given interval. (b) Find \(c\) such that \(f_{\text {and }}=f(c)\). (c) Sketch the graph of \(f\) and a rectangle whose area is the same as the area under the graph of \(f\) $$ f(x)=(x-3)^{2}, \quad[2,5] $$
Problem 10
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to \(x\) or \(y .\) Draw a typical approximating rectangle and label its height and width. Then find the area of the region. $$ y=\sin x, \quad y=2 x / \pi, \quad x \geqslant 0 $$
Problem 10
If the work required to stretch a spring \(1 \mathrm{ft}\) beyond its natural length is \(12 \mathrm{ft}-\mathrm{lb}\), how much work is needed to stretch it 9 in. beyond its natural length?
Problem 10
(a) Find the average value of \(f\) on the given interval. (b) Find \(c\) such that \(f_{\text {and }}=f(c)\). (c) Sketch the graph of \(f\) and a rectangle whose area is the same as the area under the graph of \(f\) $$ f(x)=1 / x, \quad[1,3] $$
Problem 10
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. $$ x=2-y^{2}, x=y^{4} ; \text { about the } y \text { -axis } $$
