- #1

Hoofbeat

- 48

- 0

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Q. If

**n**is the uni normal to the surface S, evaluate Double Integral

**r**.

**n**dS over the surface of a sphere of radius 'a' centred at the origin.

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So I did:

**r**= (x,y,z)

Sphere: x^2 + y^2 + z^2 = a^2

let f = x^2 + y^2 + z^2

**n**=

**grad**f / |

**grad**f|

therefore

**n**= (x,y,z)/a

**n.r**= a

Now how do I proceed with the integral? I thought it would just be

int(2pi->0) int (pi->0) int(a->0) a r.dr.d[theta].d[phi]

which gives the answer [pi]^2.[a]^3 which really doesn't look right! I think it's the actual integral I've made a mistake with! HELP! I HATE VECTOR CALCULUS [and I really need to learn to use latex!]