Question

Express V=∭ dV, as two iterated integrals if R is the region in the first octant bounded by u^2+v^2+w^2/n=(n+1),w=0 and coordinate planes. Sketch their separate neat graphs and shade the bounded regions. Then evaluate any one of them. Where n is the sum of first and last digit of your arid number e.g. 19-arid-665 take n=6+5=11​

Answer 1

Answer:

Express V=∭ dV, as two iterated integrals if R is the region in the first octant bounded by u^2+v^2+w^2/n=(n+1),w=0 and coordinate planes. Sketch their separate neat graphs and shade the bounded regions. Then evaluate any one of them. Where n is the sum of first and last digit of your arid number e.g. 19-arid-665 take n=6+5=11

Answer 2

• Earlier in this chapter we showed how to convert a double integral in rectangular coordinates into a double integral in polar coordinates in order to deal more conveniently with problems involving circular symmetry. A similar situation occurs with triple integrals, but here we need to distinguish between cylindrical symmetry and spherical symmetry. In this section we convert triple integrals in rectangular coordinates into a triple integral in either cylindrical or spherical coordinates.
• Earlier in this chapter we showed how to convert a double integral in rectangular coordinates into a double integral in polar coordinates in order to deal more conveniently with problems involving circular symmetry. A similar situation occurs with triple integrals, but here we need to distinguish between cylindrical symmetry and spherical symmetry. In this section we convert triple integrals in rectangular coordinates into a triple integral in either cylindrical or spherical coordinates.Also recall the chapter opener, which showed the opera house l’Hemisphèric in Valencia, Spain. It has four sections with one of the sections being a theater in a five-story-high sphere (ball) under an oval roof as long as a football field. Inside is an IMAX screen that changes the sphere into a planetarium with a sky full of 9000 twinkling stars. Using triple integrals in spherical coordinates, we can find the volumes of different geometric shapes like these.

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