imo class 12 definite integration

A steel plant in Bhilai has a production rate given by P'(t) = 50 + 4t tonnes/hour. What is the total steel produced in the first 5 hours?

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A steel plant in Bhilai has a production rate given by P'(t) = 50 + 4t tonnes/hour. What is the total steel produced in the first 5 hours?

  • A. 300 tonnes
  • B. 250 tonnes
  • C. 350 tonnes
  • D. 200 tonnes

Answer: A) 300 tonnes

Explanation: Total production = ∫[0 to 5] (50 + 4t) dt = [50t + 2t²] from 0 to 5 = 250 + 2(25) = 250 + 50 = 300 tonnes.

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