# SFU MATH 152 Calculus II: Syllabus, Topics and Practice

> A study guide for SFU MATH 152 (Calculus II): Riemann sums, the Fundamental Theorem, integration techniques, differential equations and series.

Source: https://practicecalculus.com/courses/simon-fraser-university-math-152
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 152
- **Units:** 3
- **Prerequisites:** MATH 150 or 151 with at least C-, or MATH 154 or 157 with at least B
- **Exclusions:** Students with credit for MATH 155 or 158 may not take MATH 152 for further credit
- **Covers:** Riemann sums, the Fundamental Theorem of Calculus, definite, indefinite and improper integrals, approximate integration, integration techniques, separable differential equations, sequences and series, power series
- **Next course:** MATH 251 (Calculus III)
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH 152 is the 3-unit Calculus II course at SFU and follows MATH 150 or 151.
- Because MATH 151 stops at derivatives, MATH 152 starts integration from Riemann sums and the Fundamental Theorem.
- It also covers improper integrals, approximate integration, separable differential equations and growth models.
- The second half is sequences and series, ending with power series and their applications.

**MATH 152** is Calculus II at Simon Fraser University, the course that follows MATH 150 or MATH 151. Since SFU's first course is all about derivatives, MATH 152 carries the full weight of integral calculus and then moves on to sequences and series. This guide maps each MATH 152 topic to free practice so you can build the skills one small problem at a time.

## What SFU MATH 152 covers

The SFU calendar lists the MATH 152 topics as: Riemann sums, the Fundamental Theorem of Calculus, definite, indefinite and improper integrals, approximate integration, integration techniques, and applications of integration; first-order separable differential equations and growth models; and sequences and series, series tests, power series, convergence and applications of power series.

That is a combination of the second half of a typical **Calculus 1** (definite integrals and the Fundamental Theorem) and most of a typical **Calculus 2**. Parametric and polar curves are not listed, because SFU already covers them in MATH 151.

## MATH 152 topic map

| MATH 152 topic | Practice | Read |
| --- | --- | --- |
| Riemann sums | [Riemann sums](/learn/calculus-1/integrals/riemann-sums) | [Riemann sums guide](/blog/riemann-sums) |
| Fundamental Theorem of Calculus | [FTC part 2](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [FTC part 1](/theorems/fundamental-theorem-of-calculus-part-1), [FTC guide](/blog/fundamental-theorem-of-calculus) |
| Indefinite integrals | [Undoing derivatives](/learn/calculus-1/integrals/undoing-derivatives) | [Antiderivatives](/blog/antiderivatives), [reverse power rule](/rules/reverse-power-rule) |
| Substitution | [u-substitution](/learn/calculus-1/integrals/u-substitution) | [u-substitution guide](/blog/u-substitution) |
| Integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts rule](/rules/integration-by-parts-rule) |
| Trig integrals and substitution | [Trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Trig substitution guide](/blog/trig-substitution) |
| Partial fractions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions guide](/blog/partial-fractions) |
| Approximate integration | [Trapezoid sums](/learn/calculus-1/integrals/trapezoid-sums) | [Riemann sums](/blog/riemann-sums) |
| Improper integrals | [Infinite limits of integration](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals](/blog/improper-integrals) |
| Applications of integration | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Separable equations and growth models | [Separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | [Logistic growth](/learn/calculus-2/improper-integrals-and-applications/logistic-growth) |
| Sequences and series tests | [Choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) | [Convergence tests](/blog/convergence-tests), [ratio test](/rules/ratio-test) |
| Power series | [Power series and radius](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Power series guide](/blog/power-series), [Taylor series](/blog/taylor-series) |

## Where MATH 152 sits at SFU

| Course | Title | Main focus |
| --- | --- | --- |
| [MATH 151](/courses/simon-fraser-university-math-151) | Calculus I | Limits, derivatives, polar and parametric curves |
| MATH 152 | Calculus II | Integration, separable ODEs, series |
| [MATH 251](/courses/simon-fraser-university-math-251) | Calculus III | Vectors and calculus of several variables |

MATH 155 and MATH 158 are alternative second courses for other programs, and you cannot take MATH 152 for credit if you already have one of them.

## Example problems at the MATH 152 level

**1. The Fundamental Theorem.** If $F(x) = \int_0^{x^2} \cos t \, dt$, then by the chain rule $F'(x) = 2x\cos(x^2)$.

**2. An improper integral.**

$$\int_1^\infty \frac{1}{x^2}\,dx = \lim_{b\to\infty}\left[-\frac{1}{x}\right]_1^b = 1$$

**3. A growth model.** Solve $\frac{dy}{dt} = 0.3y$ with $y(0) = 50$. Separating variables gives $y = 50e^{0.3t}$.

**4. Radius of convergence.** For $\sum \frac{x^n}{n\,3^n}$, the ratio test gives $\frac{|x|}{3} < 1$, so the radius is $R = 3$.

## How to do well in MATH 152

- **Learn to pick the method.** Integration problems rarely say which technique to use. Practice mixed sets like [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) so you learn to recognise the shape of each integral.
- **Keep derivatives sharp.** Every antiderivative is a derivative read backwards, so weak derivative rules make integration slow.
- **Write the test you are using.** For each series, name the test and check its conditions before you conclude. Graders look for this.
- **Practise little and often.** Short, frequent sessions in [practice](/practice) beat long cramming sessions before midterms.

> **Tip:** before choosing a convergence test, try the [nth term test](/rules/nth-term-test). If the terms do not go to zero, the series diverges and you are done.

## Frequently asked questions

### What is SFU MATH 152?

MATH 152 is Calculus II at Simon Fraser University. The calendar lists Riemann sums, the Fundamental Theorem of Calculus, definite, indefinite and improper integrals, approximate integration, integration techniques, applications of integration, first-order separable differential equations and growth models, and sequences and series up to power series.

### What do I need to take MATH 152?

MATH 150 or MATH 151 with a minimum grade of C-, or MATH 154 or MATH 157 with a minimum grade of B. Students with credit for MATH 155 or 158 cannot also take MATH 152 for credit.

### Is MATH 152 harder than MATH 151?

Many students find it harder, because it combines two big topics: all of integration and all of series. Integration techniques reward lots of practice, and series need careful reasoning about which convergence test fits.

### What comes after MATH 152?

MATH 251, Calculus III, which covers vectors, curves in space and calculus of several variables. SFU recommends taking linear algebra (MATH 240 or 232) before or alongside it.