A numerical value:
Area under the graph of a
function for some interval.
The limit of a function ƒ(x) is L as L approaches a
limx → a ƒ(x) = L
∫ƒ(x) dx.
integral of f of x dx.
Integral of a constant n isƒ(x) = 6, then ∫ƒ(x) = 6x + C
nx + C.
ƒ(x) = xn, then ∫ƒ(x)dx is:
xn + 1 | |
n + 1 |
ƒ(x) | ƒ'(x) | Domain |
---|---|---|
sin(x) | -cos(x) | -∞ < x < ∞ |
cos(x) | sin(x) | -∞ < x < ∞ |
tan(x) | -Ln cos(x) | x ≠ π/2 + πn, n ∈ Ζ |
csc(x) | Ln(csc(x) - cot(x)) | x ≠ πn, n ∈ Ζ |
sec(x) | Ln(sec(x) - tan(x)) | x ≠ π/2 + πn, n ∈ Ζ |
cot(x) | Ln sin(x) | x ≠ πn, n ∈ Ζ |
ƒ(x) | ƒ'(x) |
---|---|
ex | ex |
ax | ax/Ln(a) where a > 0, a ≠ 1 |
Ln(x) | 1/x |
logax | x * Ln(x) - x |