Integrals

Integrals compute accumulated quantities such as areas, volumes, and total change. This topic covers integration techniques including the power rule, u-substitution, integration by parts, trigonometric substitution, and partial fractions, plus geometric applications like area between curves, volumes of revolution, and arc length.

Integration is used in physics to compute work and energy, in engineering for structural analysis, in probability for finding distributions, and in economics for total cost and surplus calculations.

Practice Tips

• 1When choosing an integration method, try u-substitution first since it applies to the widest range of problems.
• 2For integration by parts, use the LIATE rule (Logarithmic, Inverse trig, Algebraic, Trigonometric, Exponential) to pick u.
• 3On definite integrals with u-substitution, convert the limits of integration along with the variable to avoid back-substituting at the end.