SUMMARY
The area under the curve of the function g(x) = e^x from the interval [0, ln(9)] is calculated using the definite integral ∫ from 0 to ln(9) of e^x dx. The evaluation of this integral yields an area of 8 square units, derived from the expression [e^(ln(9))] - [e^(0)] = 9 - 1. This straightforward calculation raises questions about the complexity typically expected in similar problems, especially given its weight of 15 out of 100 points in the lab assignment.
PREREQUISITES
- Understanding of definite integrals
- Familiarity with the exponential function e^x
- Knowledge of the Fundamental Theorem of Calculus
- Basic algebraic manipulation skills
NEXT STEPS
- Study the Fundamental Theorem of Calculus in detail
- Practice evaluating definite integrals of exponential functions
- Explore applications of integrals in calculating areas under curves
- Investigate common pitfalls in integral calculus problems
USEFUL FOR
Students studying calculus, particularly those focusing on integral calculus and the evaluation of areas under curves, as well as educators preparing lab assignments in mathematics.