Folha Pratica 6 A Ii
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Matemática II INTEGRAIS DEFINIDOS 26. Calcule os seguintes integrais definidos: 3
26.1.
∫0
26.2.
3 2 ∫ 1 (x − 3x ) dx
x 2 dx
26.13.
)
26.15.
26.4.
∫ (− 3x
26.5.
∫ (5x
26.6.
2 3 ∫ 1 (2 − 3x ) dx
26.7.
26.10.
26.11.
26.12.
MATEMÁTICA II
− x dx
2
−1 2
0
−1
∫− 3
26.8. .
26.9.
3
4
∫1
3
2
+ x dx
)
− 3 x + 6 dx
1 1 2 − 3 dx x x
1 dx x
8 3 ∫ 1 (1 + x ) dx 10
∫2
3
∫−2 4
∫0
3 dx 5x − 1 −1 x e2
3 4 ∫ 0 [1 + sen( 2 x )] cos( 2 x )dx 2
∫− 2 1
1 dx x +4 2
7x − 2 dx 7 x − 4x + 3
26.16.
∫0
26.17.
∫0
1
2x + 1 dx x2 +1
π
sen x
26.18.
26.19.
26.20.
26.21.
dx 26.22.
1 dx x+5
cos x dx
π
)
∫ −1 (2 x
2
∫π
2
26.14.
26.3.
1
3 π 4
26.23.
2006/2007
2
∫π (1 − cos x )3 2 e2
∫e 3
∫2
1 dx x ln x
(
− 8e x dx 1+ ex
4
x2 + 4 dx x2 +1
3
1 dx x −x
∫0
∫2
)
x 4 ln 2 x 5 − 5 dx x5 − 5
2
∫0
dx
2
15
ESCOLA SUPERIOR DE TECNOLOGIA
26.24.
26.25.
26.26.
4
∫2
2
∫1
e
∫1
π
INFORMÁTICA PARA A SAÚDE
x3 dx x −1 4x − 4 dx x 4 + 4x 2 1 dt 2 t +t4
26.27.
∫0
26.28.
2 2 x +1 ∫− 1 (x + 1) e dx
x cos x dx
∫0
26.33.
∫0
26.34.
∫0
26.35.
∫ −3
26.36.
∫0
0
2
26.29.
26.30.
26.31.
π
∫1
3
∫1
1 2
∫0
x arc tg x dx
π
26.32.
26.37.
1
1
3
1
1
∫0
e 2 x sen x dx 1 1− x2
dx
4 − x 2 dx x
dx
9 − x2 x 1+ x2 x3 1+ x2
dx
dx
ln x dx
arc sen x dx
CÁLCULO DE ÁREAS 27. Calcule a área da região limitada pelas funções: 27.1.
y + x 2 = 6 e y + 2x − 3 = 0
27.4.
y2 = x e y = x − 2
27.2.
y = x 2 e y = −x
27.5.
y = x2 e y2 = x
27.3.
y = x2 − 4 e y = −x2 + 4
27.6.
2y2 = x + 4 e y2 = x
MATEMÁTICA II
2006/2007
16
26.1.
∫0
26.2.
3 2 ∫ 1 (x − 3x ) dx
x 2 dx
26.13.
)
26.15.
26.4.
∫ (− 3x
26.5.
∫ (5x
26.6.
2 3 ∫ 1 (2 − 3x ) dx
26.7.
26.10.
26.11.
26.12.
MATEMÁTICA II
− x dx
2
−1 2
0
−1
∫− 3
26.8. .
26.9.
3
4
∫1
3
2
+ x dx
)
− 3 x + 6 dx
1 1 2 − 3 dx x x
1 dx x
8 3 ∫ 1 (1 + x ) dx 10
∫2
3
∫−2 4
∫0
3 dx 5x − 1 −1 x e2
3 4 ∫ 0 [1 + sen( 2 x )] cos( 2 x )dx 2
∫− 2 1
1 dx x +4 2
7x − 2 dx 7 x − 4x + 3
26.16.
∫0
26.17.
∫0
1
2x + 1 dx x2 +1
π
sen x
26.18.
26.19.
26.20.
26.21.
dx 26.22.
1 dx x+5
cos x dx
π
)
∫ −1 (2 x
2
∫π
2
26.14.
26.3.
1
3 π 4
26.23.
2006/2007
2
∫π (1 − cos x )3 2 e2
∫e 3
∫2
1 dx x ln x
(
− 8e x dx 1+ ex
4
x2 + 4 dx x2 +1
3
1 dx x −x
∫0
∫2
)
x 4 ln 2 x 5 − 5 dx x5 − 5
2
∫0
dx
2
15
ESCOLA SUPERIOR DE TECNOLOGIA
26.24.
26.25.
26.26.
4
∫2
2
∫1
e
∫1
π
INFORMÁTICA PARA A SAÚDE
x3 dx x −1 4x − 4 dx x 4 + 4x 2 1 dt 2 t +t4
26.27.
∫0
26.28.
2 2 x +1 ∫− 1 (x + 1) e dx
x cos x dx
∫0
26.33.
∫0
26.34.
∫0
26.35.
∫ −3
26.36.
∫0
0
2
26.29.
26.30.
26.31.
π
∫1
3
∫1
1 2
∫0
x arc tg x dx
π
26.32.
26.37.
1
1
3
1
1
∫0
e 2 x sen x dx 1 1− x2
dx
4 − x 2 dx x
dx
9 − x2 x 1+ x2 x3 1+ x2
dx
dx
ln x dx
arc sen x dx
CÁLCULO DE ÁREAS 27. Calcule a área da região limitada pelas funções: 27.1.
y + x 2 = 6 e y + 2x − 3 = 0
27.4.
y2 = x e y = x − 2
27.2.
y = x 2 e y = −x
27.5.
y = x2 e y2 = x
27.3.
y = x2 − 4 e y = −x2 + 4
27.6.
2y2 = x + 4 e y2 = x
MATEMÁTICA II
2006/2007
16
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