Integral Definition:
A numerical value:
Area under the graph of a
function for some interval.
Limit of a Function Notation:
The limit of a function ƒ(x) is L as L approaches a
limx → a ƒ(x) = L
Integral Notation:
∫ƒ(x) dx.
integral of f of x dx.
Integral of a constant rule:
Integral of a constant n is
nx + C.
ƒ(x) = 6, then ∫ƒ(x) = 6x + C
Integral power rule:
ƒ(x) = xn, then ∫ƒ(x)dx is:
Integral power rule example:
ƒ(x) = x
2Using the power rule with n = 2
∫ƒ(x) = x
2 + 1/(2 + 1) = x
3/3
Trigonometric Integrals
| 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 |
Logarithmic Integrals
| ƒ(x) | ƒ'(x) | | ex | ex |
| ax | ax/Ln(a) where a > 0, a ≠ 1 |
| Ln(x) | 1/x |
| logax | x * Ln(x) - x |
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