Evaluate .
Answer and explanation
Correct answer: C.
- Step 1: Substitute . When , . When , . The integral becomes \int_0^1 u^2 \, du = \left[ \frac{u^3}{3} ight]_0^1 = \frac{1^3}{3} - 0 = \frac{1}{3}. **Answer: . Why not the others:** " unit evaluation" evaluates at without integrating to ; " quadratic power" integrates as instead of ; " exponential factor" leaves the variable in the numerator after boundary substitution.
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