On Feb 11 we worked at first on the homework problems. We started then into finding the volume of an object that we could not find by rotating. Several of the groups tried quick ideas including rotating only certain parts or finding an equation for a cross section of their object but none worked. With the help of Mr. Hansen the groups progressed from their failed attempts into the basic the integration process(see class notes). They sliced the object into pieces; they approximated each piece; they solved an integral of their approximations. This was the upper or lower bound for the actual volume of the object and so the groups' next task was to find a more accurate approximation or to find the opposite bound, preferable both. Before the class's groups could take that step however class finished and Mr. Hansen said that their would be a way to integrate an unrevolvable object to find a satisfactory volume that is accurate.
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On Feb 11 we worked at first on the homework problems. We started then into finding the volume of an object that we could not find by rotating. Several of the groups tried quick ideas including rotating only certain parts or finding an equation for a cross section of their object but none worked. With the help of Mr. Hansen the groups progressed from their failed attempts into the basic the integration process(see class notes). They sliced the object into pieces; they approximated each piece; they solved an integral of their approximations. This was the upper or lower bound for the actual volume of the object and so the groups' next task was to find a more accurate approximation or to find the opposite bound, preferable both. Before the class's groups could take that step however class finished and Mr. Hansen said that their would be a way to integrate an unrevolvable object to find a satisfactory volume that is accurate.
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