Ejercicio1
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The document discusses two calculations of the volume of a solid: 1) The volume of a disc bounded by the parabola x + y = 3 and the x-axis is 9π. 2) The volume of the shell bounded by the same parabola and the planes y = 0 and y = 3 is also 9π.
![Disco
3
Vx = π [−x + 3]2 dx
0
3
= π (x 2 − 6x + 9)dx
0
3
x3
= π − 3x 2 + 9x
3 0
= 9πu 3
2. Corteza
3
Vx = 2π y (−y + 3)dy
0
3
= 2π (−y 2 + 3y )dy
0
3
y3 y2
= 2π − +3
3 2 0
= 9πu 3](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Ejercicio1
- 1. Universidad de La Frontera TEMUCO 02 Junio 2010 Margareth Sep´lveda C. - Miguel Pichipill´n S. u a x + y = 3, x = 0, y = 0 en torno al eje x 1.
- 2. Disco 3 Vx = π [−x + 3]2 dx 0 3 = π (x 2 − 6x + 9)dx 0 3 x3 = π − 3x 2 + 9x 3 0 = 9πu 3 2. Corteza 3 Vx = 2π y (−y + 3)dy 0 3 = 2π (−y 2 + 3y )dy 0 3 y3 y2 = 2π − +3 3 2 0 = 9πu 3