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Math
Calculus 2
McGraw Hill
Pearson
Cengage
Houghton Mifflin Harcourt
John Wiley & Sons
Dummies (Wiley)
* Taken from Stewart Calculus
Applications of Integration
- Areas between curves
- Volumes
- Volumes by cylindrical shells
- Work
- Average value of a function
Techniques of Integration
- Integration by parts
- Trigonometric integrals
- Trigonometric substitution
- Integration of rational functions by partial fractions
- Strategy for integration
- Integration using tables and computer algebra systems
- Approximate integration
- Improper integrals
Further applications of integration
- Arc length
- Area of a surface of revolution
- Applications to physics and engineering
- Applications to economics and biology
- Probability
Differential Equations
- Modeling with differential equations
- Direction fields and euler's method
- Seperable equations
- Models for population growth
- Linear equations
- Predator-prey sytems
Parametric equations and polar coordinates
- Curves defined by parametric equations
- Calculus with parametric curves
- Polar coordinates
- Areas and lengths in polar coordinates
- Conic sections
- Conic sections in polar coordinates
Infinite Sequences and Series
- Sequences
- Series
- The integral test and estimates of sums
- Comparison tests
- Alternating series
- Absolute convergence and the ratio and root tests
- Strategy for testing series
- Power series
- Representations of functions as power series
- Taylor and Maclaurin series
- Applications of taylor polynomials
Equations
\begin{equation}
A = \lim_{n \to \infty} \sum_{i = 1}^{n} [f(x_i^*) - g(x_i^*)] \Delta x \qquad \textnormal{ (Area between two curves)}
\end{equation}
\begin{equation}
A = \int_a^b [f(x) - g(x)] \, dx \qquad \textnormal{ (Area between two curves)}
\end{equation}
\begin{equation}
V = \lim_{n \to \infty} \sum_{i = 1}^{n} A(x_i^*) \Delta x = \int_a^b A(x) \, dx \qquad \textnormal{ (Volume)}
\end{equation}
\begin{equation}
V = 2 \pi r h \Delta r \qquad \textnormal{ (Volume by shells)}
\end{equation}
\begin{equation}
V = \int_a^b 2 \pi x f(x) dx \qquad \textnormal{ with} \quad 0 \leq a \lt b \qquad \textnormal{ (Volume by shells)} \\
\end{equation}
\begin{equation}
W = \lim_{n \to \infty} \sum_{i = 1}^{n} f(x_i^*) \Delta x = \int_a^b f(x) \, dx \qquad \textnormal{ (Work)}
\end{equation}
\begin{equation}
f_{avg} = \frac{1}{b-a} \int_a^b f(x) \, dx \qquad \textnormal{ (Average value of f)}
\end{equation}