Gregarius » Home - watchmath.com

Home - watchmath.com

How To Integrate By Parts

Posted: June 7th, 2011, 4:02am MDT

Integration by parts is a direct consequence of the product rule for the derivative and teh fundamental theorem of calculus. Recall that the product rule says that \[(fg)'=f'g+fg'\]Solving for $fg'$ we have \[fg'=(fg)'-f'g\] By integrating both sides we have \[\int f(x)g'(x)\,dx=f(x)g(x)-\int g(d) f'(x)\,dx\] Denoting $u:=f(x)$ and $dv:=g'(x)\,dx$, the above integral is more popular in the form \[\int u\,dv=uv-\int v\,du\]
How To Integrate By Substitution

Posted: June 7th, 2011, 2:08am MDT

The substitution method based on the fact that under a certain nice condition about $f(x)$ and $g(x)$ we have that \[\int f(g(x))g'(x)dx=\int f(u) du\] where $u=g(x)$. From the statement above, in many cases it is clear how to choose the $u$, namely the inner function of the composition function. On the videos below we will discuss how to do integration by substitution. In particular we discuss how to select the right $u$ in many situations. On the third video we discuss two challenging problems that we solve by substitution method.
How to Compute Area

Posted: June 7th, 2011, 1:27am MDT

Here we discuss how to compute area using integral. We discuss when we should integrate with respect to a certain variable (y or x) by looking how the boundary of the area looks like. Should you have any question about how to compute area please go to the Ask&watch tab and ask your question there
Related Rates

Posted: March 21st, 2011, 12:42pm MDT
How To Use Distance Formula

Posted: September 28th, 2009, 8:49am MDT

Given two points $(x_1,y_1)$ and $(x_2,y_2)$ on the plane, the distance between these two points is the length of the line segment connecting the two points. By using the Pythagorean's theorem one can derived that the distance between the two points is given by
$d:=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
The videos below will demonstrate how to derive this formula as well how to apply this formula
How To Find Midpoint of a Line Segment

Posted: September 28th, 2009, 8:41am MDT

Given the coordinates of the end points of a line segment, say $(x_1,y_1)$ and $(x_2,y_2)$, the coordinates of the midpoint of the segment can be calculated by taking average of the $x$ and $y$ coordinated of the two points, i.e. $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.
Here are some videos to demonstrate how to use this formula.
WHS7

Posted: September 11th, 2009, 8:21am MDT
WHS6

Posted: September 11th, 2009, 8:21am MDT
WHS5

Posted: September 11th, 2009, 8:20am MDT
WHS4

Posted: September 11th, 2009, 8:18am MDT
WHS3

Posted: August 26th, 2009, 6:51am MDT
WHS 1

Posted: August 26th, 2009, 6:32am MDT
The Music of The Primes

Posted: August 7th, 2009, 8:11am MDT

Documentary about the exploration of the world of prime numbers and their importance in natural phenomenons and technology.
High Anxieties - The Mathematics of Chaos

Posted: August 6th, 2009, 7:12am MDT

Documentary about how complex systems are ultimately unknowable and unpredictable.

← Manzanas Entrelazadas Diario Cultural →

Gregarius » Home - watchmath.com

Feeds

Home - watchmath.com

Posted: June 7th, 2011, 4:02am MDT

Posted: June 7th, 2011, 2:08am MDT

Posted: June 7th, 2011, 1:27am MDT

Posted: March 21st, 2011, 12:42pm MDT

Posted: September 28th, 2009, 8:49am MDT

Posted: September 28th, 2009, 8:41am MDT

Posted: September 11th, 2009, 8:21am MDT

Posted: September 11th, 2009, 8:21am MDT

Posted: September 11th, 2009, 8:20am MDT

Posted: September 11th, 2009, 8:18am MDT

Posted: August 26th, 2009, 6:51am MDT

Posted: August 26th, 2009, 6:32am MDT

Posted: August 7th, 2009, 8:11am MDT

Posted: August 6th, 2009, 7:12am MDT