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Georgia Tech MATH 1552 Integral Calculus: Study Guide and Practice

A study guide for Georgia Tech MATH 1552 (Integral Calculus): integrals, integration techniques, improper integrals and infinite series, with practice.

Georgia Tech Updated 3 min read

At a glance

Course code
MATH 1552
Credits
4 credit hours
Covers
Definite and indefinite integrals, techniques of integration, improper integrals, infinite series and applications
Credit restrictions
No credit for both MATH 1552 and MATH 1502, MATH 1504, MATH 1512 or MATH 1555
Practice here
Calculus 1 integrals units plus Calculus 2
On this page
  1. What MATH 1552 covers
  2. MATH 1552 topic map
  3. MATH 1552 in the Georgia Tech calculus courses
  4. Example problems at the MATH 1552 level
  5. How to do well in Georgia Tech MATH 1552

Georgia Tech MATH 1552 is Integral Calculus, a 4-credit-hour course that covers everything about integration in one variable, from the first antiderivative to infinite series. It is the integral counterpart to MATH 1551 (Differential Calculus). This guide maps every MATH 1552 topic to free practice, so you can learn each technique by solving problems with instant feedback.

What MATH 1552 covers

According to the Georgia Tech catalog, MATH 1552 covers definite and indefinite integrals, techniques of integration, improper integrals, infinite series and applications. Credit is not awarded for both MATH 1552 and MATH 1502, MATH 1504, MATH 1512 or MATH 1555.

That scope is wider than a standard Calculus 2 course. It begins with material many universities teach at the end of Calculus 1 (antiderivatives, Riemann sums and the Fundamental Theorem of Calculus), then moves through the integration techniques, improper integrals and series of Calculus 2.

MATH 1552 topic map

MATH 1552 topic Practice Read
Indefinite integrals Undoing derivatives Antiderivatives, reverse power rule
Definite integrals and Riemann sums Area with rectangles Riemann sums, definite integral properties
Fundamental Theorem of Calculus Evaluating definite integrals Fundamental Theorem of Calculus, FTC part 1
Substitution U-substitution u-substitution
Integration by parts Integration by parts Integration by parts
Trig integrals and trig substitution Trig substitution Trig substitution
Partial fractions Partial fractions Partial fractions
Improper integrals Integrands that blow up Improper integrals
Applications of integration Volumes with disks Area between curves, volumes of revolution
Sequences and series Geometric series Geometric series, nth-term test
Convergence tests Choosing a test Convergence tests, ratio test
Power and Taylor series Taylor polynomials Power series, Taylor series

MATH 1552 in the Georgia Tech calculus courses

Course Credit hours Focus
MATH 1551 (Differential Calculus) 2 Limits of functions and sequences, derivatives and applications
MATH 1552 (Integral Calculus) 4 Integrals, integration techniques, improper integrals, series
MATH 2550 (Introduction to Multivariable Calculus) 2 Several variables, without vector calculus
MATH 2551 (Multivariable Calculus) 4 Several variables, including vector analysis

If derivatives feel rusty, review the MATH 1551 guide. For calculus in several variables, continue with the MATH 2551 guide.

Example problems at the MATH 1552 level

1. A substitution integral. Let u = x^2 + 1, so du = 2x\,dx:

\int 2x(x^2 + 1)^3\,dx = \int u^3\,du = \frac{(x^2 + 1)^4}{4} + C

2. Partial fractions. Since \frac{1}{x(x + 1)} = \frac{1}{x} - \frac{1}{x + 1},

\int \frac{1}{x(x + 1)}\,dx = \ln|x| - \ln|x + 1| + C = \ln\left|\frac{x}{x + 1}\right| + C

3. The ratio test. For \sum_{n=1}^{\infty} \frac{n}{2^n},

\lim_{n \to \infty} \frac{(n + 1)/2^{n+1}}{n/2^n} = \lim_{n \to \infty} \frac{n + 1}{2n} = \frac{1}{2} < 1

so the series converges.

How to do well in Georgia Tech MATH 1552

  • Learn to pick the technique. The hard part of integration is deciding what to try. Our choosing a strategy lesson trains exactly that.
  • Check by differentiating. Every indefinite integral can be verified by taking its derivative, a habit that catches most sign and constant errors.
  • Build a series decision list. Know when to use the nth-term, comparison, integral, alternating and ratio tests. The convergence tests guide lays them side by side.
  • Keep formulas close. The calculus formula sheet collects integrals and series on one page.
  • Practice under exam conditions with practice exams, and review common calculus mistakes first.

Tip: if a series term looks like \frac{\text{polynomial}}{\text{exponential}}, reach for the ratio test first. The exponential almost always wins.

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Undoing derivatives

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Frequently asked questions

What is MATH 1552 at Georgia Tech?
MATH 1552 is Integral Calculus, a 4-credit-hour course. The catalog lists definite and indefinite integrals, techniques of integration, improper integrals, infinite series and applications.

Is MATH 1552 the same as Calculus 2?
Mostly, but it also starts earlier. Because Georgia Tech teaches derivatives separately in MATH 1551, MATH 1552 begins with antiderivatives and the definite integral, which many schools teach at the end of Calculus 1, then continues into integration techniques and series.

Is MATH 1552 hard?
It covers a lot: the whole of integration plus infinite series. Series in particular feel different from earlier calculus because you decide whether a sum converges rather than computing an answer. Regular mixed practice is the most reliable way through it.

How should I prepare for MATH 1552?
Make sure derivatives are automatic, especially the chain rule, since every antiderivative is a derivative read backwards. Then practice basic antiderivatives and u-substitution before the course starts.

What should I study after MATH 1552?
The catalog lists MATH 2551 (Multivariable Calculus) and MATH 2550 (Introduction to Multivariable Calculus) for calculus in several variables. Check your degree requirements for which one applies to you.

Written by the PracticeCalculus team

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Related university courses

Georgia Tech MATH 1551 Calculus 1 Differential Calculus A study guide for Georgia Tech MATH 1551 (Differential Calculus): limits of functions and sequences, derivatives and applications, with practice. Georgia Tech MATH 2551 Calculus 3 Multivariable Calculus A study guide for Georgia Tech MATH 2551 (Multivariable Calculus): linear approximation, Lagrange multipliers, multiple integrals and vector analysis.