f : (a, b) R F f F
F = f
F f F + c c " R
f (F + c) = F = f
f : (a, b) R f
f
f(x)dx
fdx
" 0dx = C
" adx = ax + C a " R x " R
xn+1
" xndx = + C n " N x " R
n+1
xn+1
" xndx = + C n " Z x " R \ {0}
n+1
xa+1
" xadx = + C a " R x " (0, +")
a+1
ax
" axdx = + C a " (0, +") x " R
ln(a)
" exdx = ex + C x " R
1
" dx = loga(x) + C a " (0, +") \ {1} x " (0, +")
xln(a)
1
" dx = ln(x) + C x " (0, +")
x
" sin(x)dx = -cos(x) + C x " R
" cos(x)dx = sin(x) + C x " R
1
" dx = tg(x) + C x " R \ {Ą + kĄ} k " Z
cos2(x) 2
1
" dx = -ctg(x) + C x " R \ {kĄ} k " Z
sin2(x)
c F (x) + c
f, g : (a, b) R
" ( f(x)dx) = f(x)
" (f + g)dx = fdx + gdx
" afdx = a fdx a " R
f, g : (a, b) R
f · g dx = fg - f · gdx
f : (a, b) R g : (c, d)
(a, b)
f(g(x)) · g (x)dx = F (g(x)) + c
 f : [a, b] R (a, b) a = x0 < x1 < . . . < xn = b
[xi, xi+1] mi Mi
f
n n
mi(xi - xi-1) Mi(xi - xi-1)
i=1 i=1
x1, . . . , xn-1
x1, . . . , xn-1
f : [a, b] R f
f [a, b] f
f [a, b]
b
f(x)dx
a
b
fdx
a
f : [a, b] R f
f
f
f
f [a, b]
b
f(x)dx y = f(x) OX
a
x = a x = b
f
b
- f(x)dx
a
f, g : [a, b] R
" f [a, b] [c, d] ‚" [a, b]
" f g [a, b]
b b b
(f + g)dx = fdx + gdx
a a a
b b
Ä…fdx = Ä… fdx Ä… " R
a a
f · g
b c b
" c " [a, b] fdx = fdx fdx
a a c
b a
" fdx = - fdx
a b
a
" fdx = 0
a
b
" Ä…dx = Ä… · (b - a)
a
a
" f fdx = 0
-a
a a
" f fdx = 2 · fdx
-a 0
f : [a, b] R f
c " [a, b]
b
fdx = f(c) · (b - a)
a
(b - a) f(c)
f : [a, b]
R f
b
f(x)dx = F (b) - F (a)
a
 f
f [a, b) b
f
" b = +"
" limxb f(x) = Ä…" f
f : [a, +") R b > a
b
[a, b] limb+" a f(x)dx
f [a, +")
+"
f(x)dx
a
+" b
f(x)dx = lim f(x)dx
b+"
a a
f (-", b]
f : [a, b) R
Ä…
[a, b) limÄ…b- fdx
a
f [a, b]
b
fdx
a
b f
[a, b)
b Ä…
f(x)dx = lim f(x)dx
Ä…b- a
a
a
+" c
f : R R c " R f(x)dx f(x)dx
c -"
f (-", +")
+" +" c
f(x)dx = f(x)dx + f(x)dx
-" c -"
[a, b]
c
f : [a, b] R c " [a, b] fdx
a
b
fdx
c
b c b Ä… b
fdx = fdx + fdx = lim fdx + lim fdx
Ä…c- a ²c+ ²
a a c