13
Calculo Integral
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EJERCICIO TRES ROSTRO
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ECUACIONES PARAMETRICAS
O 1. = 6 cos = 6()
0 SEMICIRCUNFERENCIA
O 2. = 0.25 cos 3 = 0.25() + 1
0 2 CIRCUNFERENICA
O 3. = 0.25() + 3 = 0.25() + 1
0 2 CIRCUNFERENICA
O 4. = 1() + 3 = 1() + 1
0 SEMICIRCUNFERENCIA
O 5. = 1() 3 = 1() + 1
0 SEMICIRCUNFERENCIA
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O 6. = 5 =
3.35 9 RECTA
O 7. = 5 =
3.35 9 RECTA
O 8. = = 0 3 RECTA
O 9. = = 0 3 RECTA
O 10. = 6 + 3
= 3 0 1 RECTA
O 11. = 3 + 3 = 3 + 3
0 1 RECTA
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O 12. = 5 + 2 = 9 3.81
0 1 RECTA
O 13. = 5 2
= 9 3.81 0 1 RECTA
O 14. = 5.66 + 3.66
= 2 + 2 0 1 RECTA
O 15. = 2 + 2 = 4 2
0 1 RECTA
O 16. = 2
= 2 + 2 0 1 RECTA
O 17. = 2 + 3.66 = 4 2.02
0 1 RECTA
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PERIMETRO DE LA FIGURA
1. Semicircunferencia 2. Circunferencia
O 1 =
2+
2
0
O Dnde:
O = 6 cos
O = 6sen()
O 1 = (6 cos )2+(6 sen )2
0
O L1= 18.84mm.
O 2 =
2+
2
0
O Dnde:
O = 0.25 cos
O = 0.25sen() O 2 =
(0.25 cos )2+(0.25 sen )2
0
O L2= 1,57mm.
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3.Circunferencia
4. Semicircunferencia
O 3 =
2+
2
0
O Dnde:
O = 0.25 cos
O = 0.25sen()
O 3 = (0.25 cos )2+(0.25 sen )2
0
O L3= 1,57mm.
O 4 =
2+
2
0
O Dnde:
O = 1 (cos )
O = 1 sen()
O 4 = (1 cos )2+(1 sen )2
0
O L4= 3.14mm.
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5. Semicircunferencia
6.Recta:
O 5 =
2+
2/2
/2
O Dnde:
O = 1 (cos )
O = 1 (sen )
O 5 = (1 cos )2+(1 sen )2
0
O L5= 3.14
O 6 =
2+
29
3.35
O Dnde:
O = 0
O = 1
O 6 = (0)2+129
3.35
O = .
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7. Recta
8. Recta:
O 7 =
2+
29
3.35
O Dnde:
O = 0
O = 1
O 7 = (0)2+129
3.35
O = .
O 8 =
2+
23
0
O Dnde:
O = 1
O = 1
O 8 = (1)2+(1)23
0
O = .
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9.Recta:
10.Recta:
O 9 =
2+
23
0
O Dnde:
O = 1
O = 1
O 9 = (1)2+(1)23
0
O = .
O
= 3;
= 3
O 10 =
2+
2
O 10 = 3 2 + 3 21
0
O = .
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11. Recta:
12.Recta:
O
= 3;
= 3
O 11 =
2+
2
O 11 = 3 2 + 3 21
0
O = .
13. Recta:
O
= 2;
= 3.81
O 13 =
2+
2
O 13 = 2 2 + 3.81 21
0
O = .
O
= 2;
= 3.81
O 12 =
2+
2
O 12 = 2 2 + 3.81 21
0
O = .
14. Recta:
O
= 3.66;
= 2
O 14 =
2+
2
O 14 = 3.66 2 + 2 21
0
O = .
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15.Recta:
16.Recta
O
= 2;
= 2
O 15 =
2+
2
O 15 = 2 2 + 2 21
0
O = .
17.Recta:
O
= 3.66;
= 2.62
O 17 =
2+
2
O 17 =
3.6 2 + 2.62 21
0
O = .
O
= 2;
= +2
O 16 =
2+
2
O 16 = 2 2 + 2 21
0
O = .
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PERIMETRO TOTAL O P=L1+L2+L3+L4+L5+L6+L7+L8+L9+L10+L11+L12+
L13+L14+L15+L16+L17.
O P=72.5
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reas Semicircunferencia
O =
0
O 1 =
0
O Dnde:
O = 3 (sin )
O 1 =
3 sin 3 sin
0
O 1 = 14.13mm2.
