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# Integrais - Parte 2

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```Ca´lculo I - Lista de Exerc´\u131cios no¯ 13 - 1
o
¯ semestre/2015
1. Calcule as integrais trigonome´tricas:
(a)
\u222b
sen 3(x) cos2(x)dx (b)
\u222b
sen 5(x) cos3(x)dx (c)
\u222b
sen 4(x) cos2 dx
(d)
\u222b
sen (5x)sen (2x)dx (e)
\u222b
sen (3x) cos(x)dx (f)
\u222b
tg 3(x) sec2(x)dx
(g)
\u222b
tg 3(x) sec5(x)dx (h)
\u222b
tg 2(t) sec4(t)dt (i)
\u222b
tg 2(x) sec3(x)dx
(j)
\u222b
cos(\u3b8) cos5(sen (\u3b8))d\u3b8 (k)
\u222b
cotg 3(y)cossec 3(y)dy (l)
\u222b
1
cos(x) \u2212 1
dx
2. Calcule as integrais usando substituic¸a\u2dco inversa:
(a)
\u222b
1
t2
\u221a
25\u2212 t2
dt (b)
\u222b
1\u221a
x2 + 16
dx (c)
\u222b
1
x2
\u221a
x2 \u2212 9
dx
(d)
\u222b
x
\u221a
1\u2212 x4dx (e)
\u222b
x arcsen (x)dx (f)
\u222b
1\u221a
9x2 + 6x\u2212 8
dx
(g)
\u222b\u221a
1\u2212 (x\u2212 1)2dx (h)
\u222b\u221a
x\u2212 x2dx (i)
\u222b
arctg (ex)
ex
dx
3. Calcule as integrais:
(a)
\u222b
ex
1+ e2x
dx (b)
\u222b \u221a
1+ lny
y
dy (c)
\u222b
1
1+
\u221a
x
dx
(d)
\u222b
sen (x) + sec(x)
tg (x)
dx (e)
\u222b
earctg (z)
1+ z2
dz (f)
\u222b
t4ln(t)dt
(g)
\u222b
x sen 2(x)dx (h)
\u222b
ex+e
x
dx (i)
\u222b\u221a
1+ x
1\u2212 x
dx
(j)
\u222b
1\u221a
x\u2212 3
\u221a
x
dx (k)
\u222b
1
3
\u221a
x+ 4
\u221a
x
dx (l)
\u222b
cos(x)
4\u2212 sen 2(x)
dx
(m)
\u222b
1
1\u2212 cos(x) + sen (x)
dx (n)
\u222b
1
sen (x) + cos(x)
dx (o)
\u222b
sen (2x)
1+ cos(x)
dx
4. Determine a soluc¸a\u2dco geral das seguintes equac¸o\u2dces diferenciais ordina´rias.
(a) y \u2032 = y (b) y \u2032 = y/x (c) y \u2032 = x2/y
(d) y \u2032 = xy3 (e) 2x+ 3yy \u2032 = 0 (f) x2y \u2032 = 1\u2212 y
5. Resolva os seguintes problemas de valor inicial.
(a) y \u2032 + y = 0, y(0) = 2 (b) xy \u2032 = 3y, y(2) = \u22128 (c) (x+ 1)y \u2032 = y, y(\u22122) = \u22123
(d) xy \u2032 + y = 0, y(1) = 1 (e) y \u2032 + 3xy = 0, y(0) = pi (f) (y+ 2)y \u2032 = sen x, y(0) = 0
UFMS / INMA Disciplina: Ca´lculo I Turmas: 1, 2, 3 e 7```