SUMMARY
The integral INT sqrt(x^2+6x) dx can be evaluated using trigonometric substitution after completing the square. The expression simplifies to (x + 3)^2 - 3^2, allowing for a substitution where the hypotenuse is x + 3 and one side is 3. This method streamlines the evaluation process and provides a clear path to the solution.
PREREQUISITES
- Understanding of integral calculus
- Familiarity with trigonometric substitution techniques
- Knowledge of completing the square in quadratic expressions
- Basic trigonometric identities and triangle properties
NEXT STEPS
- Study trigonometric substitution methods in integral calculus
- Practice completing the square with various quadratic equations
- Explore the use of triangles in solving integrals
- Learn about different techniques for evaluating definite and indefinite integrals
USEFUL FOR
Students studying calculus, particularly those focusing on integration techniques, and educators looking for effective methods to teach integral evaluation.