SUMMARY
The integral of (e^cost)(sin2t)dt can be solved using substitution and integration by parts. The recommended substitution is u = cos(t), which simplifies the integral to 2∫e^(cos(t))cos(t)sin(t)dt. This approach utilizes the trigonometric identity sin(2t) = 2sin(t)cos(t) to facilitate the integration process. The integration by parts method is then applied to solve the resulting integral.
PREREQUISITES
- Understanding of integration techniques, specifically integration by parts.
- Familiarity with trigonometric identities, particularly sin(2t) = 2sin(t)cos(t).
- Knowledge of substitution methods in calculus.
- Proficiency in handling exponential functions in integrals.
NEXT STEPS
- Study the method of integration by parts in detail.
- Learn about trigonometric identities and their applications in integration.
- Practice substitution techniques with various integrals.
- Explore advanced integration techniques involving exponential functions.
USEFUL FOR
Students studying calculus, particularly those focusing on integration techniques, as well as educators looking for effective methods to teach integration by parts and substitution.