Final answer:
Integration by Parts and Partial Fraction Decomposition are methods used in calculus to solve integration problems. The Trapezoidal Rule and Simpson's Rule are numerical integration methods.
Step-by-step explanation:
Integration by Parts and Partial Fraction Decomposition are two methods used in calculus to solve integration problems. Integration by Parts is used when the integral involves a product of two functions, while Partial Fraction Decomposition is used when the integrand can be expressed as a sum of simpler fractions.
The Trapezoidal Rule and Simpson's Rule are numerical integration methods. The Trapezoidal Rule approximates the area under a curve by forming trapezoids, while Simpson's Rule uses a quadratic function to approximate the curve.