Practice question · Multiple choice
To integrate over a ball of radius centred at the origin, which coordinate system makes the limits simplest, and why?
Hints
- The dream scenario is constant limits, a coordinate box. Which system’s coordinates does the sphere’s equation () collapse into?
- In spherical coordinates that equation reads simply .
Show the answer
B. Spherical: the ball becomes a box in
Why
Match the coordinates to the region’s symmetry and curved boundaries flatten into constant limits: the ball is literally a rectangular box in . The price, the volume factor , is far cheaper than nested square roots.
Practise Triple Integrals
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More questions on Triple Integrals
- ∫ 0¹ ∫ 0¹ ∫ 0¹ xyz dz dy dx = ? Set the slider to your answer.
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- Match each physical quantity to the triple integral that computes it (over a solid E of density ρ(x,y,z)).
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