Definite Integrals with Substitution

User is interested in definite integrals with substitution.Definite integrals with substitution, a fundamental concept in calculus, are a powerful tool for finding the area under a curve. By replacing variables in the integrand with new variables, this technique simplifies complex integrals into more manageable forms. Substitution allows us to transform the integral into a standard form that can be easily evaluated, often involving trigonometric or algebraic functions. This method not only facilitates the calculation of integrals but also provides insights into the relationships between different functions. Understanding how to apply substitution effectively is essential for solving a wide range of problems in calculus and mathematical analysis.