MATH1011 - Lecture 15

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MATH1011 - Lecture 14
Skeleton Slides

Geometric Meaning of a Triple Integral

• If $f(x,y,z)\le 0$ on some solid $R$ and $f$ is continuous on $R$, then $\underset{R}{\iiint }fdV$ represents 4D volume of a 4D solid “below” graph of $f$ in the space ${\mathbb{R}}^4$
  • If $f=1$ then the triple integral represents a 3D volume

Integration Over Solids

• See Slides $\underset{R}{\iiint }f(x,y,z)dV=\underset{S}{\iint }\left({\int }_{g_1(x,z)}^{g_2(x,z)}f(x,y,z)dy\right)dxdz$

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MATH1011 - Lecture 16
Annotated Slides