Northwestern MATH 220-2 Integral Calculus: Topics and Practice
A study guide for Northwestern MATH 220-2 Single-Variable Integral Calculus: the Fundamental Theorem, techniques, improper integrals and first-order ODEs.
Northwestern University Updated 3 min read
At a glance
- Course code
- MATH 220-2
- Units
- 1 unit
- Offered
- Not stated on the First-Year Focus page
- Prerequisites
- MATH 218-2, MATH 220-0 (former) or MATH 220-1
- Covers
- Definite integrals, antiderivatives and the Fundamental Theorem, transcendental and inverse functions, areas and volumes, techniques of integration, numerical integration, improper integrals, and first-order linear and separable ODEs
- Next course
- MATH 226-0 (Sequences and Series) or MATH 230-1 (Multivariable Differential Calculus)
- Practice here
- Calculus 1 integrals units and Calculus 2
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On this page
Northwestern MATH 220-2, Single-Variable Integral Calculus, is the second course in Northwestern's standard calculus sequence. Where MATH 220-1 is all about derivatives, 220-2 is all about integrals: what they mean, how to compute them and how to use them. This guide maps each topic to free practice with instant feedback.
What MATH 220-2 covers
Northwestern's course description lists: definite integrals, antiderivatives, and the fundamental theorem of calculus; transcendental and inverse functions; areas and volumes; techniques of integration, numerical integration, and improper integrals; and first-order linear and separable ordinary differential equations. The course is worth one unit, and the prerequisite is MATH 218-2, MATH 220-0 (former) or MATH 220-1.
In semester terms, MATH 220-2 covers the integration half of Calculus 1 plus the integration techniques and differential equations of Calculus 2. The other part of a typical Calculus 2 course, series, lives in a separate course, MATH 226-0.
MATH 220-2 topic map
| MATH 220-2 topic | Practice | Read |
|---|---|---|
| Definite integrals | Riemann sums | Riemann sums guide |
| Antiderivatives | Reverse power rule | Antiderivatives |
| Fundamental Theorem of Calculus | Fundamental Theorem, part 2 | FTC part 2 |
| Transcendental and inverse functions | Inverse trig derivatives | Integral of 1/(1+x²) |
| Areas | Area between curves | Area between curves guide |
| Volumes | Volumes with disks | Volumes of revolution |
| Substitution | U-substitution | U-substitution guide |
| Integration by parts | Integration by parts | Integration by parts guide |
| Trig substitution and partial fractions | Partial fractions | Trig substitution |
| Numerical integration | Trapezoid sums | Riemann sums practice |
| Improper integrals | Integrating to infinity | Improper integrals |
| Separable ODEs | Separable equations | Differential equations practice |
| Growth models | Growth and decay | Natural exponential function |
First-order linear equations, solved with an integrating factor, are also on the list. They build directly on the integration techniques above.
Where 220-2 fits in the sequence
The department places students with a 4 on AP Calculus AB (or the AB subscore of BC) into MATH 220-2. After 220-2, students outside the McCormick School of Engineering usually take MATH 230-1 for multivariable calculus, and engineering students take MATH 228-1. MATH 226-0, Sequences and Series, requires 220-2 or 218-3 and is required for mathematics and statistics majors and minors, but the department notes it is not required for most science and engineering majors.
Example problems at the MATH 220-2 level
1. An inverse trig integral.
2. Partial fractions.
3. A first-order linear ODE. For y' + y = 1, the integrating factor e^x gives (ye^x)' = e^x, so y = 1 + Ce^{-x}.
How to do well in MATH 220-2
- Understand the Fundamental Theorem deeply. Almost every later topic depends on it, so work through both parts.
- Build a technique checklist. Practice choosing a strategy until you can name the method in seconds.
- Sketch areas and solids. A quick drawing prevents most setup mistakes in area and volume problems.
- Use the quarter rhythm. Ten weeks is short, so daily practice beats weekend cramming.
Next, see the MATH 230-1 guide for multivariable calculus.
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Evaluating definite integrals
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