Definite Integral Property Traps
Test whether you apply the standard properties of definite integrals under the conditions each one actually requires.
Fourteen questions cover swapping the limits, the king property, even and odd functions on symmetric intervals, the two f(2a − x) conditions, integrals over n periods, and the functions that must be split before integrating.
Ends with the cases where the Newton–Leibniz formula simply does not apply.
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Sample questions3 of 14 shown
Q1
While solving, a student interchanges the limits of integration and writes ∫ from a to b of f(x) dx = ∫ from b to a of f(x) dx. What is the correct relation?
Q2
A student wants to use the 'king' property on ∫ from 0 to a of f(x) dx. Which replacement is the correct one?
Q3
f is an even function. A student claims that because the interval [−a, a] is symmetric, the integral must vanish. What is the correct value of ∫ from −a to a of f(x) dx?
What This Quiz Covers
- Swapping the limits and the sign
- The king property f(a − x)
- Even and odd on a symmetric interval
- f(2a − x) = f(x) against = −f(x)
- Modulus and floor functions must be split
- When Newton–Leibniz does not apply
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