Calculus Question

Question

This is similar to a problem in the textbook.  

Oil is leaking out of a ruptured tanker at a rate of r=17e^4t gallons per hour. Write a definite integral that represents the total quantity of oil which leaks out of the tanker in the first 3 hours. Using your formula answer the following questions: 

A. Estimate the integral using a left hand sum with 3 subdivisions of equal length. Round your answer to one decimal place. 

Answer: 

B. Use your calculator to estimate the 'exact' amount. (Your calculator does not give the exact value, therefore your answer to this question is also an approximation, but much more precise than the one you gave in part A. In this case round your answer to two decimal places.) 

Answer: 

Answer 1

A. q(3) = ∫₀³17e^4tdt ≈ L₃ = (17·1 + 17e⁴·1 + 17e⁸) = 17(1 + e⁴ ++ e⁸) = 51621.5 gal

B q(3) = ∫₀³17e^4tdt = 691703.6 gal