331. Compute divergence theorem for D= 5r2 /4 i in spherical coordinates between r=1 and r=2. a) 80π b) 5π c) 75π d) 85π

# 331. Compute divergence theorem for D= 5r2 /4 i in spherical coordinates between r=1 and r=2. a) 80π b) 5π c) 75π d) 85π

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331. Compute divergence theorem for D= 5r2 /4 i in spherical coordinates between r=1 and r=2. a) 80π b) 5π c) 75π d) 85π

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Answer: c

Explanation: ∫∫ ( 5r2

/4) . (r2 sin θ dθ dφ), which is the integral to be evaluated. Since it is

double integral, we need to keep only two variables and one constant compulsorily.

Evaluate it as two integrals keeping r = 1 for the first integral and r = 2 for the second

integral, with φ = 0→2π and θ = 0→ π. The first integral value is 80π, whereas second

integral gives -5π. On summing both integrals, we get 75π.

Answer: c

Explanation: ∫∫ ( 5r2/4) . (r2 sin θ dθ dφ), which is the integral to be evaluated. Since it is double integral, we need to keep only two variables and one constant compulsorily. Evaluate it as two integrals keeping r = 1 for the first integral and r = 2 for the second integral, with φ = 0→2π and θ = 0→ π. The first integral value is 80π, whereas secondintegral gives -5π. On summing both integrals, we get 75π.

Answer: c

Explanation: ∫∫ ( 5r2

/4) . (r2 sin θ dθ dφ), which is the integral to be evaluated. Since it is

double integral, we need to keep only two variables and one constant compulsorily.

Evaluate it as two integrals keeping r = 1 for the first integral and r = 2 for the second

integral, with φ = 0→2π and θ = 0→ π. The first integral value is 80π, whereas second

integral gives -5π. On summing both integrals, we get 75π

c) 75π

Answer: c

Explanation: ∫∫ ( 5r2

/4) . (r2 sin θ dθ dφ), which is the integral to be evaluated. Since it is

double integral, we need to keep only two variables and one constant compulsorily.

Evaluate it as two integrals keeping r = 1 for the first integral and r = 2 for the second

integral, with φ = 0→2π and θ = 0→ π. The first integral value is 80π, whereas second

integral gives -5π. On summing both integrals, we get 75π.

Answer: c

Explanation: ∫∫ ( 5r2

/4) . (r2 sin θ dθ dφ), which is the integral to be evaluated. Since it is

double integral, we need to keep only two variables and one constant compulsorily.

Evaluate it as two integrals keeping r = 1 for the first integral and r = 2 for the second

integral, with φ = 0→2π and θ = 0→ π. The first integral value is 80π, whereas second

integral gives -5π. On summing both integrals, we get 75π.