Chapter 5: Problem 1
Constant Force In Exercises 1 and 2 , determine the work done by the constant force. A 100 -pound bag of sugar is lifted 10 feet.
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Sketch the region bounded by the graphs of the algebraic functions and find the area of the region. $$ f(y)=y^{2}+1, g(y)=0, \quad y=-1, \quad y=2 $$
Find the accumulation function \(F\). Then evaluate \(F\) at each value of the independent variable and graphically show the area given by each value of \(F\). $$ F(\alpha)=\int_{-1}^{\alpha} \cos \frac{\pi \theta}{2} d \theta \quad \text { (a) } F(-1) \quad \text { (b) } F(0) \quad \text { (c) } F\left(\frac{1}{2}\right) $$
If the portion of the line \(y=\frac{1}{2} x\) lying in the first quadrant is revolved about the \(x\) -axis, a cone is generated. Find the volume of the cone extending from \(x=0\) to \(x=6\).
In Exercises \(27-34,\) (a) use a graphing utility to graph the region bounded by the graphs of the equations, \((b)\) find the area of the region, and (c) use the integration capabilities of the graphing utility to verify your results. $$ f(x)=x\left(x^{2}-3 x+3\right), \quad g(x)=x^{2} $$
Sketch the region bounded by the graphs of the functions, and find the area of the region. $$ f(x)=\cos x, \mathrm{~g}(x)=2-\cos x, 0 \leq x \leq 2 \pi $$
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