Let p = ∫_a^b f(x) dx and q = ∫_a^b |f(x)| dx. If f(x) = e^(-x), then which one of the following is correct?
Answer
The correct answer is D: p = q. Since e^(-x) > 0 for all real x, |e^(-x)| = e^(-x). Therefore |f(x)| = f(x), which gives ∫_a^b |f(x)| dx = ∫_a^b f(x) dx, so p = q.
A.p = 2q
B.p = -q
C.4p = q
D.p = q✓ Correct
Explanation
Since e^(-x) > 0 for all real x, |e^(-x)| = e^(-x). Therefore |f(x)| = f(x), which gives ∫_a^b |f(x)| dx = ∫_a^b f(x) dx, so p = q.
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