SUMMARY
The integral of √(3 - x^2) from 0 to 3/2 can be solved using trigonometric substitution. The correct substitution is x = √3 sin(t), which leads to dx = √3 cos(t) dt. It is essential to adjust the limits of integration accordingly when applying this substitution. Utilizing trigonometric identities will facilitate the evaluation of the final integral.
PREREQUISITES
- Understanding of integral calculus
- Familiarity with trigonometric functions and identities
- Knowledge of substitution methods in integration
- Ability to change limits of integration during substitution
NEXT STEPS
- Practice trigonometric substitution in integrals
- Explore the use of trigonometric identities in integration
- Learn about changing limits of integration in substitution
- Study advanced techniques for evaluating definite integrals
USEFUL FOR
Students studying calculus, particularly those focusing on integration techniques, and educators looking for examples of trigonometric substitution in definite integrals.