Calculus II Study Guide

Integration Review and U-Substitution

Master u-substitution techniques and review fundamental integration rules essential for all advanced integration methods.

Integration by Parts

Learn the product rule in reverse for integrating products of functions, including tabular method and repeated applications.

Trigonometric Integrals and Substitution

Evaluate integrals involving trigonometric functions and use trig substitution to handle radical expressions.

Partial Fractions and Improper Integrals

Decompose rational functions for integration and evaluate integrals with infinite limits or discontinuous integrands.

Applications of Integration: Volumes

Calculate volumes of solids of revolution using disk, washer, and cylindrical shell methods.

Applications of Integration: Arc Length, Surface Area, and Work

Compute arc lengths, surface areas of revolution, work, and hydrostatic force using definite integrals.

Sequences and Their Convergence

Analyze sequences for convergence, boundedness, and monotonicity using limit laws and formal definitions.

Infinite Series and Convergence Tests

Determine series convergence using geometric, p-series, comparison, ratio, root, and alternating series tests.

Absolute and Conditional Convergence

Distinguish between absolute and conditional convergence and understand implications for series manipulation and rearrangement.

Power Series

Find radius and interval of convergence, differentiate and integrate power series term by term.

Taylor and Maclaurin Series

Construct Taylor series, estimate remainders, and use common expansions for function approximation and limits.

Parametric Equations and Polar Coordinates

Perform calculus on parametric curves and compute areas and arc lengths in polar coordinates.