# UMN MATH 1272 Calculus II: Topics, Study Guide and Practice > A study guide for MATH 1272 at the University of Minnesota: integration techniques, polar coordinates, Taylor polynomials and vectors, with practice. Source: https://practicecalculus.com/courses/university-of-minnesota-math-1272 Updated: 2026-11-03 ## At a glance - **Course code:** MATH 1272 - **Credits:** 4 - **Offered:** Every fall, spring and summer - **Prerequisites:** MATH 1271 or equivalent, with a grade of at least C- - **Covers:** Techniques of integration, calculus of transcendental functions, polar coordinates, Taylor polynomials, vectors and curves in space, cylindrical and spherical coordinates - **Next course:** MATH 2263 (Multivariable Calculus) - **Practice here:** [Calculus 2](/learn/calculus-2) plus the vectors unit of [Calculus 3](/learn/calculus-3) ## Key takeaways - MATH 1272 is the 4-credit Calculus II course at the University of Minnesota Twin Cities, offered every fall, spring and summer. - It focuses on integration techniques, transcendental functions, polar coordinates and Taylor polynomials. - It also starts three-dimensional work: vectors, curves in space, and cylindrical and spherical coordinates. - You need MATH 1271 (or an equivalent) with at least a C-, and MATH 1272 leads into MATH 2263. **MATH 1272** is Calculus II at the University of Minnesota Twin Cities, the second course in the sequence that starts with MATH 1271. It is a 4-credit course offered every fall, spring and summer, taken by students in science, engineering, math and economics who need more calculus. This guide maps every MATH 1272 topic to free practice, so you can learn each method by working problems with instant feedback. ## What MATH 1272 covers According to the University of Minnesota catalog, MATH 1272 covers techniques of integration and calculus involving transcendental functions and polar coordinates. It then moves on to Taylor polynomials and to the start of three-dimensional calculus: vectors, curves in space, and cylindrical and spherical coordinates. Compared with a standard **Calculus 2** course, MATH 1272 shares the integration techniques, polar coordinates and Taylor polynomials. Its catalog description does not list infinite series by name, but instead adds vectors and space curves, topics that many universities place at the start of **Calculus 3**. That gives MATH 2263 a head start. ## MATH 1272 topic map | MATH 1272 topic | Practice | Read | | --- | --- | --- | | Substitution review | [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](/blog/integration-by-parts) | | Trig integrals and trig 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) | | Choosing a technique | [Choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) | [Integration by parts rule](/rules/integration-by-parts-rule) | | Transcendental functions | [Exponentials and logarithms](/learn/calculus-1/derivative-rules/exponential-and-log-derivatives) | [Natural logarithm](/functions/natural-logarithm), [arctangent](/functions/arctangent) | | Polar coordinates | [Polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-coordinates) | [Area in polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-area) | | Taylor polynomials | [Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/taylor-polynomials) | [Taylor series](/blog/taylor-series), [Taylor's theorem](/theorems/taylors-theorem) | | Vectors in space | [The dot product](/learn/calculus-3/vectors-and-space/dot-product) | [Vectors, dot and cross product](/blog/vectors-dot-and-cross-product) | | Curves in space | [Curves and motion](/learn/calculus-3/vectors-and-space/curves-and-motion) | [Parametric curves](/learn/calculus-2/power-series-parametric-polar/parametric-curves) | | Cylindrical and spherical coordinates | [Cylindrical and spherical](/learn/calculus-3/multiple-integrals/cylindrical-spherical) | [Double integrals](/blog/double-integrals) | ## MATH 1272 vs MATH 1271 vs MATH 2263 | Course | Main focus | Prerequisite | | --- | --- | --- | | MATH 1271 Calculus I | Derivatives and first integrals | Placement, or C- in MATH 1151 or 1155 | | MATH 1272 Calculus II | Integration techniques, polar, Taylor polynomials, vectors | MATH 1271 or equivalent, C- or better | | MATH 2263 Multivariable Calculus | Functions of several variables and vector calculus | MATH 1272, 1372 or 1572, C- or better | If you are coming from MATH 1271, see the [MATH 1271 guide](/courses/university-of-minnesota-math-1271) for a refresher list. The [MATH 2263 guide](/courses/university-of-minnesota-math-2263) shows how the vectors you meet here turn into partial derivatives and multiple integrals. ## Example problems at the MATH 1272 level **1. Integration by parts.** Evaluate $\int x\cos x\,dx$ with $u = x$ and $dv = \cos x\,dx$, so $du = dx$ and $v = \sin x$: $$\int x\cos x\,dx = x\sin x - \int \sin x\,dx = x\sin x + \cos x + C$$ **2. Partial fractions.** Evaluate $\int \frac{1}{x^2 - 1}\,dx$. Since $\frac{1}{(x-1)(x+1)} = \frac{1/2}{x-1} - \frac{1/2}{x+1}$: $$\int \frac{dx}{x^2 - 1} = \frac{1}{2}\ln|x - 1| - \frac{1}{2}\ln|x + 1| + C$$ **3. A Taylor polynomial.** The degree 2 Taylor polynomial of $e^x$ at $0$ is $T_2(x) = 1 + x + \frac{x^2}{2}$. It estimates $e^{0.1} \approx 1 + 0.1 + 0.005 = 1.105$, while the true value is about $1.10517$. ## How to do well in MATH 1272 - **Sort integrals before you solve them.** Spend time on [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy): most exam integrals are hard only until you spot the technique. - **Memorize the core antiderivatives.** Keep the [calculus formula sheet](/formulas) open while practicing until the table is in your head. - **Check answers by differentiating.** Every antiderivative can be verified in under a minute, which catches most sign and constant errors. Our [common calculus mistakes](/blog/common-calculus-mistakes) list shows the usual traps. - **Get comfortable in three dimensions early.** Vectors and space curves lead straight into MATH 2263, so practice the [dot product](/learn/calculus-3/vectors-and-space/dot-product) and [cross product](/learn/calculus-3/vectors-and-space/cross-product) now. - **Simulate exams** with timed [practice](/practice) sets of mixed integrals. > **Tip:** if integration by parts keeps going in circles, use the LIATE order to pick $u$. Our [repeated parts and LIATE](/learn/calculus-2/integration-techniques/repeated-parts-and-liate) lesson walks through it. ## Frequently asked questions ### What is MATH 1272 at the University of Minnesota? MATH 1272 is Calculus II on the Twin Cities campus. It covers techniques of integration, calculus with transcendental functions, polar coordinates and Taylor polynomials, and it introduces vectors, space curves, and cylindrical and spherical coordinates. ### What do I need before MATH 1272? The catalog asks for MATH 1271 or an equivalent course, completed with a grade of at least C-. ### What comes after MATH 1272? MATH 2263, Multivariable Calculus. It accepts MATH 1272, 1372 or 1572 with a grade of at least C-. ### Is MATH 1272 harder than MATH 1271? Many students find Calculus II harder because integration has no single recipe: you have to recognize which technique fits. The fix is volume of practice, so that choosing between substitution, parts and partial fractions becomes quick. ### How should I prepare for MATH 1272? Make sure derivatives and basic u-substitution are fast and reliable, then start on integration by parts. The integrals unit of the free Calculus 1 path on PracticeCalculus is a good refresher.