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Calculus II
Integral Rules
12 terms · by ineedtostudy · updated 4 hours ago
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Terms in this set
Power rule for integrals
∫xⁿ dx = x^(n+1)/(n+1) + C, for n ≠ −1
∫(1/x) dx
ln|x| + C — the case the power rule cannot handle.
∫eˣ dx
eˣ + C
∫sin x dx
−cos x + C
∫cos x dx
sin x + C
∫sec² x dx
tan x + C
Integration by substitution
Reverses the chain rule. Let u = g(x), then du = g′(x) dx.
Integration by parts
∫u dv = uv − ∫v du. Reverses the product rule.
Fundamental theorem of calculus
If F′ = f then ∫ from a to b of f = F(b) − F(a). Differentiation and integration are inverse operations.
Definite vs indefinite
A definite integral is a number and needs no constant; an indefinite one is a family of functions and needs + C.
∫(1/(1+x²)) dx
arctan x + C
Improper integral
One with an infinite limit or an infinite discontinuity; evaluated as a limit and either converges or diverges.