SUMMARY
The function f(a) = a² is integrable on the interval [0, 1] by the definition of Riemann integrability. To prove this, one can utilize step functions and the partition of the interval into n subintervals. The integral can be computed as ∫f(a) da from 0 to 1, resulting in a value of 1/3. The discussion emphasizes the importance of understanding the definition of integrability in the context of Riemann sums.
PREREQUISITES
- Understanding of Riemann integrability
- Familiarity with step functions
- Knowledge of partitioning intervals
- Basic calculus concepts, including integration
NEXT STEPS
- Study the definition and properties of Riemann integrability
- Learn how to construct and evaluate Riemann sums
- Explore the concept of step functions in integration
- Practice computing definite integrals of polynomial functions
USEFUL FOR
Students in calculus courses, mathematics educators, and anyone seeking to understand the fundamentals of Riemann integration.