The Chapter 6 Test has been Moved

By popular demand in class today, Prof. Newberry moved the Ch. 6 Test from Thursday to Friday.

One more day to study! Don't waste it!

When to use which method of finding volumes

When it's clear that, when using the disk/washer method, you will be able to define the function variable in terms of the differentiation variable, you can use that method.

Illustration: the way to calculate volume with the disk method is pi∫(A to B)[F(x)^2-f(x)^2]dy , requiring a translation of [F(x)^2 - f(x)^2] into terms of y; finding F inverse and f inverse.

Otherwise, you should use the cylindrical shells, which have integration in terms of the same variable as the function inside.

Click on one of the "Math Notes" pictures, and then click "View All" after it sends you to Picasa, and you will see that one of the pictures shows the table that Prof. Newberry set up, showing when to use the disk/washer method and when to use the cylindrical shell method.

The idea of the disk method is ∫pi(radius squared)(thickness), or pi ∫ f(x)^2 dx .

When there is a hole in the middle, the washer method is used: 

∫ [pi (big radius squared) - pi (little radius squared)] (thickness) , 

or pi ∫ [F(x)^2 - f(x)^2] dx .

The cylindrical shell method fully takes care of whether and where there is a hole using the limits of the integration, which show where the outermost and innermost radii end. 

The integral is written: 

∫ (circumference)(height)(thickness) , 

or ∫ (2 pi radius)(F(x) - f(x)) dx , 

or 2 pi ∫ ( x - [axis] )( F(x) - f(x) ) dx

Wondering what "The Survey" is?

Prof. Newberry has been announcing and asking for "The Survey" in class.

If you are doing your Honors Project with the IAC (Instructional Assistance Center), then there's a survey that you are expected to fill out. At least, I think it's the IAC - it might be one of the other campus bureaucracies. Anyway, it's something about the Honors Project, if you're doing it with one of the offices on campus.

Any Test Problems from 5.4?

Does anyone remember whether the professor promised any problems on the test from 5.4?

I remember when he wrote what's in the picture below on the board, he said he would show us which types of problems from 5.4 he would give us on the test, but I do not remember whether he followed through with that. 

Anyone remember? Please comment

In Case You Haven't Yet Memorized the Trig Function Derivatives

The way I remember them is:

1. sine and cosine are mutual derivatives (almost; see rule 2)
2. every co- function has a minus sign in its derivative
3. when working with secant or tangent, you get the derivative of the one by multiplying the other by secant
4. when working with cosecant or cotangent, you get the derivative of one by multiplying the other by cosecant (very similar to rule 3)

If anyone else has good, easy to remember rules, or improvements on these, please comment.