Calculus & Analytic Geometry II, MTH 169  

(Instructor: M. USMAN) 

Lab#1 

Instructions:Please type all inputs  and reproduce these examples presented here then solve the homework problems listed at the end of this Lab.  

Objectives: In this lab we will find the volume of solids using method of integration. We need to include the package "Student[Calculus1])". 

>	with(Student[Calculus1]):

 

>	VolumeOfRevolution(x^2, x=0..3,  axis = horizontal, output = plot,volumeoptions = [style = wireframe, color=blue], axes = boxed);

 

>	VolumeOfRevolution(x^2, x=0..3,  axis=horizontal, output=integral);

 

>

evalf(%);

 

 

 

	(1)

 

>	VolumeOfRevolution( exp(-x^2), x=0..3,  axis=horizontal, output=plot,volumeoptions = [style = wireframe, color=blue], axes = boxed);

 

>	VolumeOfRevolution(exp(-x^2), x=0..3, axis=horizontal,output=integral);

 

>

evalf(%);

 

 

 

	(2)

 

>	VolumeOfRevolution(x, x^2, x=0..1, axis=horizontal,output=integral);

 

>	VolumeOfRevolution(x, x^2, x=0..1, axis=horizontal, output=plot,volumeoptions = [style = wireframe, color=blue], axes = boxed);

 

>

evalf(%);

 

If we wish to rotate our region about the axis x = -3, then we make the following change: 

>	VolumeOfRevolution( 4*x-x^2, x^2, x=0..2, axis=vertical,distancefromaxis = -3, output=plot,volumeoptions = [style = wireframe, color=blue], axes = boxed);

 

Ex 6.2(Q#8) 

>	VolumeOfRevolution(1/4*x^2, 5-x^2, x=-2..2, axis=horizontal, output=plot,volumeoptions = [style = wireframe, color=blue], axes = boxed);

 

>	VolumeOfRevolution(1/4*x^2, 5-x^2, x=-2..2, axis=horizontal, output=integral);

 

(3)

 

>

evalf(%);

 

(4)

 

Ex 6.2(Q#14) 

>	VolumeOfRevolution( 1/x, 0, x=1..3, axis=horizontal,distancefromaxis = -1, output=plot,volumeoptions = [style = wireframe, color=blue], axes = boxed);

 

>	VolumeOfRevolution(1/x, 0,x=1..3, axis=horizontal,distancefromaxis = -1, output=integral);

 

 

	(5)

 

>

evalf(%);

 

(6)

 

>