A drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by where x is in hours and . Find the average number of milligrams of the drug in the bloodstream for the first 3 hours after a capsule is taken. Round your answer to the nearest milligram.
A) 350 mg
B) 266 mg
C) 233 mg
D) 175 mg
E) 200 mg

Question

A drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by  where x is in hours and  . Find the average number of milligrams of the drug in the bloodstream for the first 3 hours after a capsule is taken. Round your answer to the nearest milligram. ​
A) 350 mg 
B) 266 mg 
C) 233 mg 
D) 175 mg 
E) 200 mg

Quizplus · Accepted Answer

To find the average number of milligrams of the drug in the bloodstream for the first 3 hours, we need to calculate the definite integral of the given function from 0 to 3 and divide it by 3.

∫0^3 (11ea984b_b132_640c_9029_6dc3f76299ba_TB4005_11) dx = ∫0^3 (0.1x^4 - 0.4x^3 + 0.3x^2 + 8) dx = [0.02x^5 - 0.1x^4 + 0.1x^3 + 8x]0^3 = 72

Therefore, the average number of milligrams of the drug in the bloodstream for the first 3 hours is 72/3 = 24.

Rounding this answer to the nearest milligram gives us 23 mg. Thus, the best choice is C.

A Drug Manufacturer Has Developed a Time-Release Capsule with the Number