MAT 251 - Calculus 2

Calculator Assignment #1

 
 

After studying Part 1, complete Part 2 and turn that in on the due date.

These instructions are for the TI-92+ or the TI-89. You may use another calculator or Derive if you prefer.

Part 1: The commands that you will need.

  1. We are going to use the shell method to find the region bounded by the curves y = x2 and y = x3 . First we will graph it:
  2. Find the [APPS] key on the keypad and press it. Go to the [Y=]application.
    		3.
    You should see both equations selected.
  3. Now press the [APPS] key on the keypad and press the [Graph] application.

    4.  
  4. You can use the [Zoom] options to see the region of intersection better.

    5.  
  5. Pick two corners that will book end the graph.

    6.  
  6. We can use the [Math] key to find the intersections of the curves.

    7.  
    Answer the questions about the curves. Be sure that the lower bound is to the left of the intersection point and the upper bound is to the right.

     
  7. Once you know the intersection points we can set up the integral. From the [HOME] screen, select [F3 Calc]. Then choose option 2 for integration.

    8.  
  8. Now enter your information, we are going to calculate the volume of the solid of revolution using the shell method. The region is to be revolved about the y-axis so the representative cross section is parallel to the y-axis.
 
 
And the answer is 0.314159.

(cut here)
Name: Date:

Part 2: You try it.

  Here are some TI-92+, TI-89, Derive and Mathematica references.
1) Find the volume of the solid of revolution formed when y = ln(x) for1£ x £2 is revolved about:
a) The x-axis b) The y-axis
c) The line y = -1 d) The line x = -2
In each case, draw the figure including the representative slice, label the endpoints,and write down the integral to be evaluated and its answer.
2) Find the volume of the solid of revolution when the region bounded by the curves y = x2 –4 and y = ln(x) is revolved about they- axis. Draw the region, label the intercepts, state the integral to be evaluated and write down the answer.
3) Find the arc length of the curve y = tan(x) for –P/3 £ x £0. Graph the region. Write down the integral to be evaluated and its result.
4) Find the surface area when the region generated by the curve y =1/3 x3+ (4 x)-1 is revolved around the x-axis between1£ x £3. Draw the region; indicate the integral to be evaluated and its answer.
5) A spring exerts a constant force of 100 N when it is stretched 0.2 m beyond its natural length. How much work is required to stretch the spring 0.8 m beyond its natural length?