Unit 6: Integration and Accumulation of Change Formulas

When there is indefinite integrals, what do you have to add to the equation?

+ C

∫ 0 dx =

C

∫ k dx =

kx + C

∫ k f(x) dx =

k ∫ f(x) dx

∫ xⁿ dx =

(xⁿ⁺¹)/(n+1) + C, where n = 1

∫ x^-1 dx or ∫ 1/x dx =

lnx + C

∫ cosx dx =

sinx + C

∫ sinx dx =

-cosx + C

∫ csc²x dx

-cotx + C

∫ sec²c dx =

tanx + C

∫ cscxcotx dx =

-cscx + C

∫ secx tanx dx =

secx + C

∫ e^x dx =

e^x + C

∫ a^x dx =

(1/ lna)a^x + C

Fundamental Theorem of Calculus

∫ f(x) dx = F(b) - F(a), where F is any antiderivative of f, that is, f = F’

d/dx [ ∫^x_a f(t) dt] =

f(t)

d/dx [ ∫^u_a f(t) dt] =

f(u) * u’