Question

if S is any closed surface enclosing a volume and F vector=xi+2yj+3zk,show that double integration f vector dr vector =6v.

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Answer 1

Answer:

As we can use Green's Theorem to prove this we will have

$\int \int F.rds = 6V$

Explanation:

As per Green's theorem we know that

$\int \int F.rds = \int {\frac{dF_x}{dx} dV + \frac{dF_y}{dy} dV + \frac{dF_z}{dz} dV}$

so we have

$\int \int F.rds = \int{\frac{dx}{dx} + \frac{d(2y)}{dy} + \frac{d(3z)}{dz} dV}$

$\int \int F.rds = \int{(1 + 2 + 3)dV}$

$\int \int F.rds = \int{6dV}$

$\int \int F.rds = 6V$

#Learn

Topic : Green Theorem

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