Midterm1 Flashcards
Integration by parts formula
uv- integral v du
LIATE
Logarithmic,Inverse Trig, Algebraic, Trig, Exponential
if integral ( p(x)sin(ax))
let u = p(x) du=the rest
sqrt( a^2 - x^2)
sub with x=asin(theta), identity: cos^2(theta)= 1- sin^2(theta)
sqrt(a^2 +x^2)
sub with x=atan(theta) sec^2(theta) = 1+tan^2(theta)
sqrt(x^2 - a^2)
sub with x=asec(theta) tan^2(theta)=sec^2(theta)-1
Integrating rational functions
if degree P(x)>=Q(x) use long division
otherwise use partial fractions
when doing partial fractions, denominator has (x-2)^2
do a variable over each power up to 2
when doing partial fractions, denominator when factored has irreducible quadrativ
make it BX+C/irreducible.
ODE
ordinary diff eq- equation containing a fcn of one variable and one or more derivatives of that fcn
order of an ODE
order of the highest derivative
Eullers Method equation
yn = yn-1+ h * F(xn-1,Yn-1)
I(x) in diffeq
e^(integral(P(x))dx)
standard form of linear 1st order ODE
dy/dx + yP(x) = Q(x)
solve a linear 1st order ODE
y* I(x) = integral(Q(x) I(x) dx)
d/dx sinx
cosx
d/dx cosx
-sinx
d/dx tanx
sec^2x
d/dx cotx
-csc^2x
d/dx secx
secxtanx
d/dx cscx
-cscxcotx
d/dx sin-1(x)
1/sqrt(1-x^2)
d/dx tan-1(x)
1/(1+x^2)
d/dx cost-1(x)
-1/sqrt(1-x^2)