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MOISES VILLENA MUÑOZ<br />
Cap 3 La Integral Definida<br />
x)<br />
lim<br />
x → 0<br />
+<br />
∫<br />
x<br />
s<strong>en</strong><br />
0<br />
⎛<br />
⎜<br />
tg ⎜ x<br />
⎜<br />
⎝<br />
2<br />
( t )<br />
3<br />
2<br />
⎞<br />
dt<br />
⎟<br />
⎟<br />
⎟<br />
⎠<br />
=<br />
1<br />
3<br />
n ⎛ 2i<br />
⎞<br />
⎜1<br />
+ ⎟<br />
2<br />
y)<br />
2<br />
lim ⎝ n<br />
e ⎠ = e − 1<br />
n→∞<br />
n ∑= i 1<br />
a+<br />
2π b+<br />
2π<br />
z) ∀a,<br />
b ∈ R,<br />
s<strong>en</strong>x dx = cos xdx<br />
∫ ∫<br />
a<br />
b<br />
2. Calcular<br />
a.<br />
b.<br />
x<br />
∫ −<br />
0<br />
lim<br />
x → 0 3<br />
x<br />
2<br />
1<br />
∫<br />
−<br />
1<br />
π<br />
( 1 cos t )<br />
2<br />
( 6 x )<br />
3<br />
2<br />
dx<br />
dt<br />
4<br />
x −<br />
i.<br />
∫<br />
3<br />
x −<br />
2<br />
ln 5<br />
j.<br />
∫<br />
2<br />
e<br />
t +<br />
ln 2<br />
21<br />
12<br />
4 dx<br />
x<br />
16<br />
k. ( x −1<br />
− 3)<br />
2 dx<br />
dt<br />
cos<br />
2<br />
xs<strong>en</strong><br />
3<br />
xdx<br />
∫− 2<br />
3<br />
c.<br />
∫ 2 0<br />
2<br />
d.<br />
∫<br />
2<br />
x + 2 x +<br />
e.<br />
3<br />
1<br />
2<br />
x<br />
s<strong>en</strong><br />
∫0<br />
lim<br />
x → 0 6<br />
x<br />
3<br />
∫<br />
dx<br />
2<br />
2<br />
( t )<br />
f. ( x − [ x ])<br />
0<br />
3<br />
2 dx<br />
g. ( x x + − x − 2 )<br />
∫− 2<br />
5<br />
h.<br />
∫ 2 + x −<br />
1<br />
1<br />
dt<br />
1 dx<br />
dx<br />
1<br />
l. 2 x + 3 dx<br />
∫− 2<br />
2π<br />
1<br />
m.<br />
∫ + cos x<br />
dx<br />
2<br />
π<br />
2<br />
n.<br />
2<br />
x<br />
s<strong>en</strong> () t<br />
dt<br />
∫<br />
2<br />
t + 1<br />
0<br />
lim<br />
x → 0 3<br />
x<br />
4<br />
− 2 x − 3<br />
o. e dx<br />
∫− 3<br />
2<br />
⎛ 3<br />
s<strong>en</strong> x<br />
⎜ 2<br />
⎝ x + 1 ∫− 2<br />
x ⎞<br />
⎟<br />
⎠<br />
( )<br />
p. ⎜ + e ⎟dx<br />
63