•••quote:•••Originally posted by Original:
•You have to use a method called "integration by parts" to integrate products
INT(udv) = uv - INT(vdu)
the trick is to express one of the terms of the products as the derivative of some "v".
hope this helps.•••••Let me add to my man Original's brilliant comments by pointing out that the order in which you assign u and v to parts of the original integral is important. In other words, the assignment of u and v is not arbitrary.
For example, lets say you have INT(x*cos x). there are 2 ways you can use integration by parts.
Method 1:
Let u = x, du = 1 dx
then dv = cos x dx, v = sin x
Then INT(x*cos x dx) = uv - int(v du) = x*sin x - int(sin x*1*dx) = x*sin x + cos x
this method is the correct way. Now look at the alternate pathway:
Method 2:
Let u = cos x, du = -sin x dx
then dv = x dx, v = 1/2x^2
int(x*cos x) = uv - int(v du) = 1/2x^2*cos x - int(1/2x^2*-sin x dx)
Note on this example that you havent really gotten anywhere. The integral you have to evaluate using this approach is just as difficult to determine as the original integral you were trying to solve (actually its slightly WORSE than the original integral)
Not that I really needed to post this, but thought I might as well add to the thoughts of my brilliant colleagues. Now, if Original (being the math major of the group) will just provide a proof of the product formula.
