Substitution with Definite Integrals

ln(x)-ln(y)=?

ln(x/y)

How do you go from -ln(1/2) → 2 inside the parentheses??

every time you multiply ln by -1, the inside becomes the reciprocal

ex) -ln(1/2) times -1 = ln(2)

(for u-sub only) what if you have 2 of the same trig functions, like cscxcotx?

Recognize if the equation is a derivative of something

ex) cscxcotx is the derivative of -cscx, so u=cscx

how do you find csc(pi/6)?

1. csc = 1/sin

2. find sin(pi/6) → ½
   

3. reverse bc it’s 1/sin → 2

Memorize unit circle

IMPORTANT NOTE: you MUST memorize 90 deg, 60, 45, and 30, otherwise you will mess up the other calculations

u-sub with definite integrals process

Image