For my part I know nothing with any certainty, but the sight of the stars makes me dream.
Vincent Van Gogh
LECTURE 10
INTEGRATION BY PART II
ANDREW MISSELDINE
7.1. Integration by Parts
Z
Example 7.1.7.
Find
ln x dx.
We have not yet determined a rule for
You cant cross the sea merely by standing and staring at the water. Rabindranath Tagore
LECTURE 5
THE LECTURE NOTES FOR THIS SECTION ARE BECOMING VOLUMINOUS
ANDREW MISSELDINE
6.2. Volume
Example 6.2.8. Find the volume of the solid of revolution formed by
The revolution is not an apple that falls when it is ripe. You have to make it fall. Che Guevara
LECTURE 4
I HOPE YOU DONT GET DIZZY EASILY
ANDREW MISSELDINE
6.2. Volume
Let y = f (x) be a positive function on the interval [a, b]. Then the function f , th
The present was an egg laid by the past that had the future inside its shell. Zora Neale Hurston
LECTURE 6
SHE SELLS SEA-SHELLS BY THE SEASHORE
ANDREW MISSELDINE
6.2. Volume
The Shell Method is a method for calculating the volume of a solid of revolution
One can never know for sure what a deserted area looks like. George Carlin
LECTURE 3
AREA BETWEEN CURVES
ANDREW MISSELDINE
5.3. The Definite Integral
Calculating the area of a geometric figure is an important application of geometry. The easiest of all
sh
Choose a job you love, and you will never have to work a day in your life. Confucius
LECTURE 7
AS IF YOU WERENT ALREADY DOING WORK
ANDREW MISSELDINE
6.4. Work
If an object moves along with position function s(t), then the force F on the object is given by
Our progress as a nation can be no swifter than our progress in education. The human mind is our
fundamental resource. John F. Kennedy
LECTURE 47
THE FUNDAMENTAL THEOREM OF CALCULUS
THE NAME SAYS IT ALL
ANDREW MISSELDINE
5.3. The Fundamental Theorem of Ca
The beginning is the most important part of the work. Plato
LECTURE 9
WE CAN FINALLY UNDO THE PRODUCT RULE!
ANDREW MISSELDINE
7.1. Integration by Parts
Integration by parts is the antiderivative version of the product rule of differentiation, which we ill
There is no substitute for hard work. Thomas A. Edison
LECTURE 2
HOW DO U SUBSTITUTE?
ANDREW MISSELDINE
5.5. The Substitution Rule
In previous sections, we discussed ways of anti-differentiating the power rule, the sum/difference rule, and
constant multip
Great minds discuss ideas; average minds discuss events; small minds discuss people. Eleanor Roosevelt
LECTURE 8
THE MEAN VALUE THEOREM REPRISE
ANDREW MISSELDINE
6.4. Work
Example 6.4.8. A tank has the shape of an inverted circular cone with height 10 m a