# Yale MATH 1150 Integral Calculus and Series: Topics and Practice

> A study guide for Yale MATH 1150: integral calculus, series convergence, Taylor series, solids of revolution, parametric and polar curves, with practice.

Source: https://practicecalculus.com/courses/yale-math-1150
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 1150 (formerly MATH 115)
- **Credits:** Not stated on the department guide
- **Offered:** Not stated on the department guide
- **Prerequisites:** The calculus placement exam, or MATH 1110 or MATH 1120 at Yale
- **Covers:** Integral calculus and net change, series convergence tests, Taylor series, solids of revolution, parametric equations, polar coordinates, and exact versus approximate answers with error
- **Next course:** MATH 1200 or MATH 1210 (multivariable calculus)
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH 1150 is Yale's integral calculus and series course, the second step in its introductory calculus sequence.
- It covers integration, series convergence tests, Taylor series, solids of revolution, parametric equations and polar coordinates.
- The course pays attention to approximate answers and the role of error, not just exact ones.
- MATH 1160 covers the same integral calculus with biology applications, and either one serves as the prerequisite for later courses.

**Yale MATH 1150** is the integral calculus course in Yale's introductory sequence, the course long known as MATH 115. The math department's guide says it investigates the mathematics of accumulation: using information about instantaneous rates, such as velocity, to compute net change, such as change in position. This guide maps every MATH 1150 topic to free practice with instant feedback.

## What MATH 1150 covers

According to the Yale math department's introductory course guide, MATH 1150 has three strands. The first is integral calculus itself, turning rates into net changes. The second is series: convergence tests and Taylor series, which the guide says help explain how calculators work. The third is a set of applications that take single-variable calculus further, including solids of revolution, parametric equations and polar coordinates.

Throughout the semester, the guide says, students consider both exact and approximate solutions and investigate the role of error. That makes MATH 1150 a close match for a standard **Calculus 2** course.

## MATH 1150 topic map

| MATH 1150 topic | Practice | Read |
| --- | --- | --- |
| Accumulation and net change | [Net change](/learn/calculus-1/applications-of-integrals/net-change) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus) |
| Substitution | [U-substitution refresher](/learn/calculus-2/integration-techniques/u-substitution-refresher) | [U-substitution](/blog/u-substitution) |
| Integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts guide](/blog/integration-by-parts) |
| Further techniques | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions guide](/blog/partial-fractions) |
| Approximate integrals and error | [Trapezoid sums](/learn/calculus-1/integrals/trapezoid-sums) | [Riemann sums](/blog/riemann-sums) |
| Solids of revolution | [Volumes with disks](/learn/calculus-1/applications-of-integrals/volumes-disks) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Sequences and series | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums) | [Geometric series](/blog/geometric-series) |
| Convergence tests | [Ratio and root tests](/learn/calculus-2/sequences-and-series/ratio-and-root-tests) | [Convergence tests](/blog/convergence-tests), [ratio test](/rules/ratio-test) |
| Taylor series | [Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Taylor series](/blog/taylor-series) |
| Error in Taylor approximations | [Estimating with Taylor](/learn/calculus-2/power-series-parametric-polar/estimating-with-taylor) | [Taylor's theorem](/theorems/taylors-theorem) |
| Parametric equations | [Parametric curves](/learn/calculus-2/power-series-parametric-polar/parametric-curves) | [Parametric and polar practice](/practice-problems/parametric-and-polar) |
| Polar coordinates | [Polar area](/learn/calculus-2/power-series-parametric-polar/polar-area) | [Polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-coordinates) |

## Placement and MATH 1160

MATH 1150 requires the placement exam, unless you completed MATH 1110 or MATH 1120 at Yale. The department says students typically place into MATH 1150 after a differential calculus course such as AP Calculus AB.

MATH 1160 is the sister course. It covers integral calculus with an emphasis on applications to biology, and the department recommends it for biology and pre-medical students. Either course can be used as the prerequisite for anything that requires MATH 1150.

## Example problems at the MATH 1150 level

**1. Net change from a rate.** If velocity is $v(t) = 3t^2$ meters per second, the change in position from $t = 0$ to $t = 2$ is

$$\int_0^2 3t^2\,dt = 8 \text{ meters}$$

**2. A geometric series.**

$$\sum_{n=0}^{\infty} \left(\frac{1}{3}\right)^n = \frac{1}{1 - \frac{1}{3}} = \frac{3}{2}$$

**3. A Taylor polynomial.** The Maclaurin series of $\sin x$ starts $x - \frac{x^3}{6} + \frac{x^5}{120}$, so $\sin(0.2) \approx 0.2 - 0.00133 = 0.19867$, with an error smaller than the next term.

## How to do well in MATH 1150

- **Think in terms of accumulation.** Every integral question gets easier if you ask what is being added up. Practice with [accumulation functions](/learn/calculus-1/integrals/accumulation-functions).
- **Learn when to use each series test.** The [choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) lesson trains exactly that decision.
- **Track your error.** The course cares about approximations, so always ask how big the error could be, using the [alternating series test](/rules/alternating-series-test) or Taylor's remainder.
- **Practice mixed sets before exams.** The [series practice](/learn/calculus-2/sequences-and-series/series-practice) mixes problem types the way exams do.

Next comes multivariable calculus: see the [MATH 1200 guide](/courses/yale-math-1200).

## Frequently asked questions

### What is Yale MATH 1150?

MATH 1150 is Yale's integral calculus course. The math department describes it as the mathematics of accumulation, with series convergence tests and Taylor series, plus solids of revolution, parametric equations and polar coordinates.

### Is MATH 1150 the same as MATH 115?

Yes, MATH 1150 is the current four-digit number for the integral calculus course long known as MATH 115.

### How do I get into MATH 1150?

Through the calculus placement exam, or by completing MATH 1110 or MATH 1120 at Yale. The department says students typically place into MATH 1150 after a differential calculus course such as AP Calculus AB.

### What is the difference between MATH 1150 and MATH 1160?

Both cover integral calculus and both satisfy any prerequisite that asks for MATH 1150. MATH 1160 emphasizes applications to biology and suits biology and pre-medical students.

### What comes after MATH 1150?

Multivariable calculus: MATH 1200, or MATH 1210 with a biology emphasis. Completing MATH 1150 or 1160 at Yale qualifies you for either.