Which statement best explains why the improper integral of f(x)=x2(−1)x from 1 to ∞ cannot be used to decide the convergence of the series n=1∑∞n2(−1)n?
a) The Integral Test requires the function to be positive, and because f(x) changes sign the test cannot be used.
b) f(x) is not defined (as a real-valued function) for non-integer x, so the improper integral ∫1∞f(x)dx is not meaningful.
c) Because the alternating signs would cause the integral to cancel out and converge to 0, even if the series diverged.
d) Since the series already converges by another test, checking an improper integral would be redundant.