Discussion
Consider the following statements about definite integrals. 1. The integral of an odd function over a symmetric interval vanishes 2. Reversing the limits reverses the sign 3. A convergent improper integral must have a bounded integrand
Answer: D
The first two are standard properties. The third fails: \( \int_{0}^{1} dx/\sqrt{x} = 2 \) converges although the integrand is unbounded at the origin. Convergence turns on how fast the integrand grows, not on whether it stays finite
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