A solar panel in a Gujarat village generates power at a rate P(t) = 2 + sin(πt/12) kW, where t is hours after 6 AM. What is the total energy generated from t=0 to t=12 hours?
A solar panel in a Gujarat village generates power at a rate P(t) = 2 + sin(πt/12) kW, where t is hours after 6 AM. What is the total energy generated from t=0 to t=12 hours?
- A. 24 + 24/π kWh
- B. 12 + 12/π kWh
- C. 24 kWh
- D. 24 - 24/π kWh
Answer: A) 24 + 24/π kWh
Explanation: Energy = ∫[0 to 12] (2 + sin(πt/12)) dt = [2t - (12/π)cos(πt/12)] from 0 to 12. = (24 - 12/π(-1)) - (0 - 12/π(1)) = 24 + 12/π + 12/π = 24 + 24/π kWh.
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