Integral rules Flashcards
∫au^ndx =
(au^n+1)/n+1 + c
∫(c+u)dx =
c = constant
∫(c)dx + ∫(u)dx + c
∫(c)dx =
c = constant
cx + c
∫(cu)dx =
c∫(u)dx
∫(sin(x))dx =
-cos(x) + c
∫(cos(x))dx =
sin(x) + c
∫(sec^2(x))dx =
tan(x) +c
∫(csc^2(x)dx =
-cot(x) + c
∫(sec(x) ⋅ tan(x))dx =
sec(x) + c
∫(csc(x) ⋅ cot(x))dx =
-csc(x) + c
∫(e^n)dx =
e^n
∫(1/x)dx =
ln|x|
What is the fundamental theorem of calculus (FTC)?
(^a)(_b)∫f(x)dx = F(b) - F(a)
d/dx[∫f(x)dx] =
f(x)
What is sigma notation?
Lim(n->∞) Σf(xi)Δx
How do you find Δx for sigma notation?
(b-a)/n
How do you find xi for sigma notation?
a + kΔx
What is another way to find a trapezoid sum besides doing the entire area calculation?
(RRAM + LRAM)/2
∫sinh(x)dx =
cosh(x) + c
∫cosh(x)dx =
sinh(x) + c
∫tanh(x)dx =
ln|cosh(x)| + c
∫sech(x)dx =
tan^-1(sinh(x)) + c
∫coth(x)dx =
ln|sinh(x)| + c
∫csch(x)dx =
ln|tanh(x/2)| + c
