# Cornell MATH 1120 Calculus II: Topics, Study Guide and Practice

> A study guide for Cornell MATH 1120 Calculus II: integration techniques, improper integrals, differential equations and Taylor series, with practice.

Source: https://practicecalculus.com/courses/cornell-math-1120
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 1120
- **Credits:** 4
- **Recently offered:** Fall and spring
- **Prerequisites:** MATH 1110 or permission of instructor
- **Covers:** Applications of integration, techniques of integration, approximate integration, improper integrals, differential equations, sequences and series, power and Taylor series, parametric equations
- **Forbidden overlap:** MATH 1910 Calculus for Engineers
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH 1120 is Cornell's Calculus II, a 4-credit course that follows MATH 1110.
- Its first half is about integration: applications, techniques, numerical integration with error estimates, improper integrals and differential equations.
- Its second half covers sequences and series, convergence tests, power series, Taylor series with remainder and parametric equations.
- Engineering students take MATH 1910 instead, and credit is not given for both.

**Cornell MATH 1120** is Calculus II at Cornell University, the course most non-engineering students take after MATH 1110. It completes single-variable calculus: integration in depth, a first look at differential equations, and infinite series. Every MATH 1120 topic is mapped below to a lesson you can practice with instant feedback.

## What Cornell MATH 1120 covers

According to the Cornell class roster, MATH 1120 centers on integration: applications such as volumes and arc length, techniques of integration, approximate integration with error estimates, improper integrals, and differential equations with their applications. It then covers infinite sequences and series, including the definition and tests for convergence, power series, Taylor series with remainder, and parametric equations.

That is a standard **Calculus 2**, with slightly more emphasis on differential equations and numerical integration than many courses. Polar coordinates are not named in the roster description.

## MATH 1120 topic map

| MATH 1120 topic | Practice | Read |
| --- | --- | --- |
| Volumes and arc length | [Arc length and surface area](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts guide](/blog/integration-by-parts), [the rule](/rules/integration-by-parts-rule) |
| Trig integrals and substitution | [Trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Trig substitution](/blog/trig-substitution) |
| Partial fractions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions](/blog/partial-fractions) |
| Approximate integration | [Area with rectangles](/learn/calculus-1/integrals/riemann-sums) | [Riemann sums](/blog/riemann-sums) |
| Improper integrals | [Integrands that blow up](/learn/calculus-2/improper-integrals-and-applications/infinite-discontinuities) | [Improper integrals](/blog/improper-integrals) |
| Differential equations | [Separable differential equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | [Antiderivatives](/blog/antiderivatives) |
| Sequences and convergence tests | [Choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) | [Convergence tests](/blog/convergence-tests) |
| Power series | [Power series and radius](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Power series](/blog/power-series) |
| Taylor series with remainder | [Estimating with Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/estimating-with-taylor) | [Taylor series](/blog/taylor-series), [Taylor's theorem](/theorems/taylors-theorem) |
| Parametric equations | [Parametric curves](/learn/calculus-2/power-series-parametric-polar/parametric-curves) | [Implicit differentiation](/blog/implicit-differentiation) |

## MATH 1120 vs MATH 1910

| Course | Designed for | Topics named on the roster |
| --- | --- | --- |
| MATH 1120 Calculus II | Students continuing from MATH 1110 | Integration applications and techniques, error estimates, differential equations, series, Taylor remainder, parametric equations |
| [MATH 1910 Calculus for Engineers](/courses/cornell-math-1910) | Engineering students | Integration techniques, areas and volumes, exponential growth, partial fractions, series, power series |

The content overlaps heavily, which is why the two are forbidden overlaps. Before MATH 1120 comes [MATH 1110 Calculus I](/courses/cornell-math-1110). Students on the math major path later take [MATH 2220 Multivariable Calculus](/courses/cornell-math-2220) after linear algebra.

## Example problems at the MATH 1120 level

**1. Integration by parts.** Evaluate $\int x e^{2x}\,dx$ with $u = x$, $dv = e^{2x}\,dx$, so $v = \frac{1}{2}e^{2x}$:

$$\int x e^{2x}\,dx = \frac{x}{2}e^{2x} - \int \frac{1}{2}e^{2x}\,dx = \frac{x}{2}e^{2x} - \frac{1}{4}e^{2x} + C$$

**2. A separable differential equation.** Solve $\frac{dy}{dx} = 3y$ with $y(0) = 2$.

Separate: $\frac{dy}{y} = 3\,dx$, so $\ln|y| = 3x + C$ and $y = Ae^{3x}$. The initial condition gives $A = 2$, so $y = 2e^{3x}$.

**3. Arc length.** The length of $y = \frac{2}{3}x^{3/2}$ from $x = 0$ to $x = 3$: since $y' = x^{1/2}$,

$$L = \int_0^3 \sqrt{1 + x}\,dx = \left[\frac{2}{3}(1 + x)^{3/2}\right]_0^3 = \frac{2}{3}(8 - 1) = \frac{14}{3}$$

## How to do well in MATH 1120

- **Build a technique checklist.** Substitution, parts, trig integrals, trig substitution, partial fractions. Practice [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) until picking the method is quick.
- **Understand the remainder, not just the series.** Taylor series with remainder is named in the roster, so practice bounding errors with [Taylor's theorem](/theorems/taylors-theorem).
- **Use the comparison families.** The [geometric series formula](/rules/geometric-series-formula) and p-series power most convergence arguments, along with the [ratio test](/rules/ratio-test).
- **Keep the [formula sheet](/formulas) next to you**, review [common calculus mistakes](/blog/common-calculus-mistakes), and finish each unit with a timed [practice exam](/practice).

> **Tip:** when an integral looks impossible, check for a substitution first. Many Calculus II integrals that look like they need parts are really u-substitution in disguise.

## Frequently asked questions

### What is Cornell MATH 1120?

MATH 1120 is Calculus II at Cornell. It focuses on integration (applications such as volume and arc length, techniques, approximate integration, improper integrals and differential equations) and then infinite sequences and series, power series, Taylor series with remainder and parametric equations.

### What is the difference between MATH 1120 and MATH 1910?

Both are second-semester calculus courses that follow MATH 1110 level calculus. MATH 1910 is the version designed for engineers and is the first course in the engineering sequence that continues to MATH 1920. The two courses are forbidden overlaps, so you get credit for only one.

### What comes after MATH 1120?

Students heading for a math major or minor typically continue to MATH 2210 Linear Algebra, which lists MATH 1110 and MATH 1120 as prerequisites, and then MATH 2220 Multivariable Calculus. Check your major requirements for the exact path.

### Is MATH 1120 hard?

Calculus II is often considered the most demanding course in a calculus sequence, because it asks you to choose among many techniques and series tests. Mixed practice, where you decide the method yourself, is the best way to build that skill.

### How do I prepare for MATH 1120?

Make sure u-substitution and the Fundamental Theorem from MATH 1110 are solid, then preview integration by parts. The u-substitution refresher on PracticeCalculus is a quick check.