SUMMARY
The integral of e^x from 0 to 3 ln2 is evaluated using the fundamental theorem of calculus. The integral is calculated as ∫ e^x dx = e^x, leading to the evaluation at the limits: e^(3 ln2) - e^0. Simplifying e^(3 ln2) results in e^(ln8), which equals 8. Therefore, the final result of the integral is 8 - 1, yielding a total of 7.
PREREQUISITES
- Understanding of integral calculus
- Familiarity with exponential functions
- Knowledge of natural logarithm properties
- Basic algebraic simplification skills
NEXT STEPS
- Study the fundamental theorem of calculus in detail
- Learn about properties of exponential functions and their integrals
- Explore natural logarithm rules and their applications
- Practice evaluating definite integrals with varying limits
USEFUL FOR
Students studying calculus, mathematics educators, and anyone looking to strengthen their understanding of integrals and exponential functions.