Trigonometric Integrals 6.3 Flashcards
what do we transform the integral of products of sin+cos and tan+sec
a u and du
when you have odd cosines, your u should be
sinx
when you have odd sines your u should be..
cos
when you have odd tangents, your u should be..
sec
When you have odd secants, your u should be..
tanx
you should keep splitting/converting until you…
have the u’s derivative by itself
sinx squared plus cos sqaured =
1
tanx squared + 1 =
secx sqaured
sinx squared =
1- cos2x /2
cos sqaured
1+ cos2x /2
How to solve odd sin
take a sin out, and convert the rest to cosine using trig identity that gives you sin^2 = 1 - cos^2
then usub
How to solve odd cos
take a cos out, and convert the rest to sin by trig identity cos^2 = 1 - sin^2 then u sub
How to solve a even sin and even cos
use fraction identities and
keep a squared inside when taking an exponent out
convert inside sine and cosine to fraction identites
When both sin and cos are odd, how you expand and what to use for u
expand the smaller one and your u is the larger exponent
what to separate with odd tangents
take out a tan and convert the rest to sec
What to separate with even secant
take out a secx squared and convert the rest to tan
What to separate with even tan
get a tanx squared to convert to sec
When youare multiplying sins and coss and your angle is not a single variable…
use it as a u
how to solve a odd tan and odd sec
get a squared of any and convert to the other type
to use the identities sin^2 = 1 - cos2x / 2 and cos^2 = 1 - cos2x + 1, you need… and how to fix it
you need a single variable without a constant as angle
to fix, use u sub then solve as you would
if you have a ax^2 +bx + c, what do you do?
complete the square
