This document provides guidance on selecting functions for integration by parts. It recommends following the LIATE hierarchy rule when choosing between logarithmic, inverse trigonometric, algebraic, trigonometric, or exponential functions for the 'u' term. Examples are given of how integration is applied in engineering contexts like designing buildings and calculating areas, masses, and fluid flows. The conclusion restates that the process involves selecting 'u' and 'v' terms, applying the integration by parts formula, and then simplifying and evaluating the integral.

1. MD. Zul Kawsar
ID: 130302005
Integration by Parts

2. Strategy Hint
• Trick is to select the correct function for u
• A rule of thumb is the LIATE hierarchy rule
The u should be first available from
• Logarithmic ( log , ln )
• Inverse trigonometric ( sin-1
x, cos-1
x)
• Algebraic ( X2
, xn
, 1,2…..)
• Trigonometric ( sin x , cos x )
• Exponential ( epower
)

3. TryThis

4. How integration applies to the
real world
• Integration was used to design
PETRONAS Towers making it
stronger
• Finding areas under curved surfaces,
Centers of mass, displacement and
Velocity, and fluid flow

5. Conclusion
• To integrate by part, select u and v.
• Next apply uv formula.
• Then, simplify the integral and evaluate.

6. Thank You

7. Thank You