reflection 1

for my academic detention :(

LN INTEGRATION:

natural log integration actually isn't as hard as it seems. msot of the time, the top of the fraction is the derivative of the bottom of your fraction, just like trina said, ex: 4/4x.. but sometimes you have to substitue in something.. like you were given 1/4x, you would need to substitute in a 4 because the derivative of 4x is 4, not 1. so your u=4x du=4dx, and you would simply but a 1/4 in front of the integration symbol. this is ln integration.

DISKS AND WASHERS:

disks are solid objects, washers are objects with holes in them (they will have two equations). you mostly just need to remember the equations for these two, which are not hard at all! volume is squared, area is not! for both disks and washers, same equation, just not squared when it asks for area.
if it asks for volume, always put a pi in front of the integral. if it asks for area, you don't put pi.

formula for volume of a disk
pi S r(x)^2dx
formula for area of a disk
S r(x)dx

r=radius. radius is your given equation. it's that easy. so pretty much plug in the equation into your formula, integrate it, and solve.

formula for volume of a washer
pi S top^2 - bottom^2 dx
formula for area of a washer
S top-bottom dx

you are given two equations.. plug both into your calculator and see which equation is on top and which is on bottom on the graph that is given.