TAMU MATH 152 Engineering Math II: Topics, Study Guide, Practice

Texas A&M MATH 152, Engineering Mathematics II, is the second calculus course for Aggie engineers and science majors. It takes the derivatives and basic integrals from MATH 151 and turns them into a full toolkit: integration techniques, physical applications, and infinite series. This page maps each MATH 152 topic to practice problems with instant feedback.

What Texas A&M MATH 152 covers

The catalog description lists differentiation and integration techniques with applications to area, volume and work, then improper integrals and approximate (numerical) integration. The course also includes analytic geometry and vectors, and it finishes with infinite series, power series and Taylor series, with a computer algebra component throughout.

That matches a standard Calculus 2 course closely. Most of the semester is integration and series, which are exactly the four units of our Calculus 2 path.

MATH 152 topic map

MATH 152 in the Texas A&M sequence

If MATH 151 feels shaky, revisit it with the MATH 151 guide first. When you finish MATH 152, the MATH 251 guide shows what comes next.

Example problems at the MATH 152 level

1. Integration by parts. Evaluate \int x\cos x\,dx. Let u = x and dv = \cos x\,dx, so du = dx and v = \sin x:

2. Work. A force F(x) = 6x newtons moves an object from x = 0 to x = 2 meters. The work is

3. A geometric series. Find the sum of \sum_{n=0}^{\infty} 5\left(\frac{1}{3}\right)^n. The ratio is r = \frac{1}{3}, so |r| < 1 and

How to do well in MATH 152

• Practice choosing the method, not just applying it. Exams mix techniques, so work through choosing a strategy once you know each one.
• Learn LIATE for parts. The integration by parts rule is fast once picking u is a habit.
• Build series intuition from geometric series. The geometric series formula and the nth-term test settle many problems before you need a heavier test.
• Keep the formula sheet open for trig identities and common integrals, and time yourself on practice exams.
• Review the classic errors in common calculus mistakes, especially forgotten constants and dropped negative signs.

Tip: for every improper integral, write the limit explicitly before integrating. It prevents the most common lost points.