Updated notes on Calculus Techniques of Integration

Techniques of integration are mathematical methods used to find the antiderivative or integral of a function. These techniques include substitution, which simplifies integrals by changing variables; integration by parts, based on the product rule for differentiation; and partial fraction decomposition, which breaks down rational functions into simpler fractions for easier integration. Trigonometric substitution is employed for integrals involving square roots of quadratic expressions, while trigonometric identities simplify integrals containing trigonometric functions. Numerical methods, such as the trapezoidal rule and Simpson's rule, approximate definite integrals when exact solutions are difficult to obtain. These techniques allow for solving a wide range of integrals in calculus and applied mathematics.