Extension Calculus – Advanced integration

This lesson comprises two (2) master classes focusing on:

• Integration by substitution
• Partial fractions
• Recurrence relationships

Content:

MEX-C1

• Find and evaluate indefinite and definite integrals using the method of integration by substitution, where the substitution may or may not be given
• Integrate rational functions involving a quadratic denominator by completing the square or otherwise
• Decompose rational functions whose denominators have simple linear or quadratic factors, or a combination of both, into partial fractions
• Use partial fractions to integrate functions
• Evaluate integrals using the method of integration by parts(
  • evelop the method for integration by parts, expressed as \( \int uv^{\prime}dx=uv− \int vu^{\prime}dx \) or \( \int u \frac{dv}{dx}dx=uv− \int v \frac{du}{dx}dx \), where \( u \) and \( v \) are both functions of \( x \)
• Derive and use recurrence relationships
• Apply these techniques of integration to practical and theoretical situations