Science:Math Exam Resources/Courses/MATH103/April 2010/Question 01 (a)
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Question 01 (a)
Multiple Choice Question: Exactly ONE of the answers provided is correct. There is no partial credit in this questions.
To which of the following integrals does the Fundamental Theorem of Calculus apply?
v. None of the above.
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The Fundamental Theorem of Calculus only applies to functions that are continuous on the entire domain of integration.
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Following the hint we check if the integrands above are continuous on the entire domain of integration.
ii. The integrand is not defined for x=0, so it is certainly not continuous on .
iii. Since is not even defined for negative numbers, the integrand is certainly not continuous on .
iv. Here the integrand is defined everywhere. As a composition of continuous functions, the integrand is continuous. Hence the Fundamental Theorem of Calculus applies here.