9a Lista de Exercı́cios - Cálculo 1
Profa. Júlia Silva Silveira Borges
1. Calcule:
R
(a)
x + 15 cos(3x) dx
R
(b) cos4 (x) dx
R
(c) (sin x + cos x)2 dx
2
R 1 1
(d)
2 + 2 cos(2x)
R
5
(e) √1−x
dx
2
R
(f) sin5 x cos x dx
R sin x
(g) cos
2 x dx
x
dx
16+x4
5
√
dx
1−4x2
√ 1
dx
4−x2
(o)
R
(ln x)2 dx
(p)
R
e−2x sin x dx
(q)
R
x3 ex dx
R
x ln x dx
(r)
R
e−x cos 2x dx
(l)
R
ln x dx
(m)
R
x2 ln x dx
(n)
R
x(ln x)2 dx
x2 sin x dx
R√
3 − 4x2 dx
(t)
R√
(u)
x2 + 9 dx
(h)
R
(i)
R
(j)
R
(k)
(s)
2. Calcule:
R 2π √
1 + cos x dx
(a) 0
R0 2 1 √
(b) 1 t (t 3 − t) dt
R1 x
(c) 0 1+x
4 dx
3. Calcule:
R
(a) x21−4 dx
R
(b) x2x−4 dx
R
x
dx
(c) x2 −5x+6
R x2 +3x+1
(d) x2 −2x−3 dx
R x2 +1
(e) (x−2)
3 dx
(d)
R2
(e)
R1
(f)
R1
(f)
R
x2 +x+1
x2 −x
(g)
R
x3 +x+1
x2 −4x+3
(h)
R
2x−3
(x−1)3
(i)
R
x+1
x(x−2)(x+3)
0
0
0
3
√x
x2 +1
2
R
dx
x2 ex dx
(sin x)cos x +1 dx
dx
dx
dx
dx
(j)
R
x+3
x3 −2x2 −x+2
(k)
R
x5 +3
x3 −4x
(l)
R
3x2 +5x+4
x3 +x2 +x−3
(m)
R
2x2 +4
x3 −8
dx
dx
dx
dx
4. Suponha que g tenha derivada contı́nua em [0, +∞) e que g(0) = 0. Verifique que
Z x
Z x
0
−st
−sx
g (t)e dt = g(x)e
+s
g(t)e−st dt
0
0
1