Integration by Parts: A Checklist for H2 Math Success

Integration by Parts is a technique used to integrate the product of two functions. Your child should consider using it when they see an integral that involves two different types of functions multiplied together, such as a polynomial and a trigonometric function (e.g., ∫x*sin(x) dx) or a logarithmic and an algebraic function (e.g., ∫ln(x)*x dx).

A helpful mnemonic is LIATE: Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, Exponential. Choose u based on this hierarchy; the function that comes first in LIATE is usually the best choice for u. The remaining part of the integral becomes dv.

Sometimes, one application of Integration by Parts isnt enough. If the new integral still involves a product of functions, your child may need to apply the technique again. Be careful to choose u and dv wisely each time.

Differentiation is your childs friend! Differentiate the result they obtained after integration. If the derivative matches the original integrand, the Integration by Parts was likely applied correctly.

Common mistakes include incorrect choice of u and dv, incorrect differentiation or integration, and forgetting the + C (constant of integration). Encourage your child to double-check their derivatives and integrals, and always include + C for indefinite integrals.

Integration by Parts is one tool in a larger toolkit of integration techniques. Its important to recognize when its appropriate to use Integration by Parts versus other methods like u-substitution or trigonometric substitution. Practice identifying the best approach for different types of integrals.