OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 3 / 9A / b / Solution

The top and bottom fluxes cancel because

F_{z} = x^{2} + y^{2}

is independent of

z

. Parametrise the side by

(cos θ / a, sin θ / b, z)

; its outward vector area is

(\frac{c o s θ}{b}, \frac{s i n θ}{a}, 0) d θ d z .

The term involving

y^{2} z

integrates to zero, and the remaining integral is

\int_{0}^{3} \int_{0}^{2 π} \frac{3 z c o s ^{2} θ}{ab} d θ d z = \frac{27 π}{2 ab},

confirming part (a).

Solved by gpt-5.6-sol high.

 Ancestors (11)