CALC 2 EXAM ONE FORMULAS Flashcards
what is intgration by parts therom
uv-∫vdu
if cosin is odd, what do you do?
save one cosin, factor, use cos^2x= 1-sin^2x
if sin is odd, what do you do?
Save one sine, factor, use sin^2x=1-cos^2x
What do you do if the sine and cosine are both even?
sin^2x=1/2(1-cos2x)
cos^2x=1/2(1+cos2x)
sinxcosx=1/2sin2x
if the power of sec is postivie. what do you do?
save a sec^2x=1+tan^2x
If the power of tan is odd what do you do?
Tan^2x=sec^2x-1
sqt/a^2-x^2
subtitute x=asinQ
identity 1-sin^2Q=cos^2Q
sqt/a^2+x^2
substitute x=atanQ
identity 1+tan^2Q=sec^2Q
sqt/x^2-a^2
substitute x=asecQ
identity sec^2Q-1=tan^2Q
What is the #1 case distinct linear factors?
x/(x+4)(x-7)
Distinct linear factors
= A/(x+4) + B/(x-7)
What is the #2 case distinct linear factors?
8/(x^2+3)(x^2+9)
Distinct irreducible quadratic factors
= Ax+B/(x^2+3) + Cx+D/(x^2+9)
What is the #3 case distinct linear factors?
2x+2/(x+5)^2
Repeated linear factors
A/x+5 + B/(x+5)^2
What is the #4 case distinct linear factors?
X^2-2/(x^2+6)^2
Repeated quadratic factors
Ax+B/X^2+6 + Cx+D/(x^2+6)^2
