application of integration exercises

Solutions to exercises 15 Exercise 2. Answer 9E. Use an exponential model to find when the population was $$\displaystyle 8$$ million. In Exercises 18-21, a solid is described. State in your own words Pascal's Principle. What is the natural length of the spring? 3) Show that $$\cosh(x)$$ and $$\sinh(x)$$ satisfy $$y''=y$$. After $$\displaystyle 10$$ minutes of resting the turkey in a $$\displaystyle 70°F$$ apartment, the temperature has reached $$\displaystyle 155°F$$. The ones from Basic methods are for initial practicing of techniques; the aim is not to solve the integrals, but just do the specified step. One very useful application of Integration is finding the area and volume of “curved” figures, that we couldn’t typically get without using Calculus. a) Set up the integral for volume using integration dx b) Set up the integral for volume using integration dy c) Evaluate (b). Level up on all the skills in this unit and collect up to 1900 Mastery points! Textbook Authors: Larson, Ron; Edwards, Bruce H. , ISBN-10: 1-28505-709-0, ISBN-13: 978-1-28505-709-5, Publisher: Brooks Cole T/F: The Shell Method works by integrating cross-sectional areas of a solid. For exercises 5-6, determine the area of the region between the two curves by integrating over the $$y$$-axis. Most of what we include here is to be found in more detail in Anton. 11) Suppose the value of $$\displaystyle 1$$ in Japanese yen decreases at $$\displaystyle 2%$$ per year. Then, use the washer method to find the volume when the region is revolved around the $$y$$-axis. $$f(x) = \frac{1}{x}\text{ on }[1,2]$$. 12) An oversized hockey puck of radius $$\displaystyle 2$$in. Region bounded by: $$y=y=x^2-2x+2,\text{ and }y=2x-1.$$ 11) [T] $$\displaystyle \frac{1}{cosh(x)}$$, Solution: $$\displaystyle −tanh(x)sech(x)$$, 13) [T] $$\displaystyle cosh^2(x)+sinh^2(x)$$, Solution: $$\displaystyle 4cosh(x)sinh(x)$$, 14) [T] $$\displaystyle cosh^2(x)−sinh^2(x)$$, 15) [T] $$\displaystyle tanh(\sqrt{x^2+1})$$, Solution: $$\displaystyle \frac{xsech^2(\sqrt{x^2+1})}{\sqrt{x^2+1}}$$, 16) [T] $$\displaystyle \frac{1+tanh(x)}{1−tanh(x)}$$, Solution: $$\displaystyle 6sinh^5(x)cosh(x)$$, 18) [T] $$\displaystyle ln(sech(x)+tanh(x))$$. Stewart Calculus 7e Solutions Chapter 8 Further Applications of Integration Exercise 8.1. For the following exercises, find the derivatives for the functions. How deep must the center of a vertically oriented square plate with a side length of 2 ft be submerged in water, with a weight density of 62.4 lb/ft$$^3$$, for the fluid force on the plate to reach 1,000 lb? Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies … 7) $$y=x^{3/2}$$ from $$(0,0)$$ to $$(1,1)$$, 8) $$y=x^{2/3}$$ from $$(1,1)$$ to $$(8,4)$$, 9) $$y=\frac{1}{3}(x^2+2)^{3/2}$$ from $$x=0$$ to $$x=1$$, 10) $$y=\frac{1}{3}(x^2−2)^{3/2}$$ from $$x=2$$ to $$x=4$$, 11) [T] $$y=e^x$$ on $$x=0$$ to $$x=1$$, 12) $$y=\dfrac{x^3}{3}+\dfrac{1}{4x}$$ from $$x=1$$ to $$x=3$$, 13) $$y=\dfrac{x^4}{4}+\dfrac{1}{8x^2}$$ from $$x=1$$ to $$x=2$$, 14) $$y=\dfrac{2x^{3/2}}{3}−\dfrac{x^{1/2}}{2}$$ from $$x=1$$ to $$x=4$$, 15) $$y=\frac{1}{27}(9x^2+6)^{3/2}$$ from $$x=0$$ to $$x=2$$, 16) [T] $$y=\sin x$$ on $$x=0$$ to $$x=π$$. For the following exercises, solve each problem. 19) The length of $$y$$ for $$x=3−\sqrt{y}$$ from $$y=0$$ to $$y=4$$. Stewart Calculus 7e Solutions Chapter 5 Applications of Integration Exercise 5.1 . (c) $$x=-1$$, 17. 55) Find the volume of a spherical cap of height $$h$$ and radius $$r$$ where \(h