MATH 2414 Help & Answers

MATH 2414 (Calculus II) is the Texas course where integration stops following a single recipe and infinite series arrive. Choosing the right technique, choosing the right convergence test and checking the endpoints are the skills that decide most grades. This page covers what the course teaches, where students lose points, two worked examples, and how we help.

Table of Contents

• About MATH 2414
• Topics Covered
• Choosing a Convergence Test
• Worked Example: Integration by Parts
• Worked Example: Interval of Convergence
• Where Students Lose Points
• Platforms
• How We Help
• FAQ

About MATH 2414

MATH 2414 (Calculus II) is a 4-credit course in the Texas Common Course Numbering System (TCCNS), the shared numbering Texas public colleges use so equivalent courses line up. Texas college catalogs describe it along these lines: differentiation and integration of transcendental functions, parametric equations and polar coordinates, techniques of integration, sequences and series, and improper integrals. Many schools require MATH 2413 (Calculus I) with a C or better as the prerequisite, so check your catalog and syllabus.

It sits in the middle of the Texas calculus sequence:

Course	What It Covers	Our Page
MATH 2413 Calculus I	Limits, derivatives, applications, introduction to integration	MATH 2413 help
MATH 2414 Calculus II	Integration techniques, applications, sequences and series, parametric and polar	You are here
MATH 2415 Calculus III	Multivariable calculus: vectors, partial derivatives, multiple integrals	Check your school catalog

Engineering, physics, chemistry, computer science and mathematics plans route through it, and so do some economics and quantitative programs. If the precalculus foundation is the weak spot, see MATH 2412 help. For the general calculus service page, see Do My Calculus Homework.

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Topics Covered in MATH 2414

Schools weight these blocks differently, but a typical semester draws from the following:

Topic	What It Covers
Integration techniques	Integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, numerical integration, improper integrals
Applications of integration	Volumes by disks, washers and shells, arc length, surface area, work, centers of mass
Sequences and series	Limits of sequences, convergence tests, absolute and conditional convergence
Power and Taylor series	Radius and interval of convergence, Taylor and Maclaurin series, approximation and error
Parametric and polar	Parametric curves, polar coordinates, area and arc length in both

Integration has no single algorithm: you recognize the form, pick a technique, and switch if the first one stalls. Series add a second kind of judgment, which is choosing the test that fits the series.

Choosing a Convergence Test

“Which test do I use?” is the most common question on series homework. The decision tree below shows how to choose between the nth term, geometric, p-series, alternating, ratio and comparison tests.

A practical order to try them:

1. nth term test first. If the terms don’t go to zero, the series diverges and you’re done.
2. Recognize the family. A geometric series or a p-series answers the question on sight.
3. Alternating signs: use the alternating series test, then check absolute convergence.
4. Factorials or exponentials: the ratio test usually fits.
5. Rational or algebraic terms: compare with a p-series, using comparison or limit comparison.
6. Positive, decreasing, easily integrated terms: the integral test.

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Worked Example: Integration by Parts

Evaluate ∫ x e^2x dx.

1. Choose u and dv with LIATE (Logarithmic, Inverse trig, Algebraic, Trigonometric, Exponential). Algebraic comes before exponential, so u = x and dv = e^2x dx.
2. Differentiate and integrate: du = dx and v = e^2x/2.
3. Apply ∫ u dv = uv − ∫ v du: x e^2x/2 − ∫ e^2x/2 dx.
4. Finish the last integral: x e^2x/2 − e^2x/4 + C.

Choosing u = e^2x instead produces ∫ x² e^2x dx, a harder integral than the one you started with. That’s the signal to switch.

Worked Example: Interval of Convergence

Find the interval of convergence of ∑ (x − 2)ⁿ / (n · 3ⁿ), n from 1 to infinity.

1. Ratio test: the limit of |a_n+1/a_n| is |x − 2|/3. It’s less than 1 when |x − 2| < 3, so the radius is 3 and the open interval is (−1, 5).
2. The ratio test is inconclusive at the endpoints, so check each one separately.
3. At x = 5 the series becomes ∑ 1/n, the harmonic series, which diverges.
4. At x = −1 it becomes ∑ (−1)ⁿ/n, the alternating harmonic series, which converges by the alternating series test.

The interval of convergence is [−1, 5). Reporting (−1, 5) skips the endpoint checks, and auto-graded platforms mark it wrong.

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Where Students Lose Points

Mistake	What Happens	The Check
Poor u and dv choice	The integral gets harder after one round of parts	Apply LIATE, and switch if the new integral is worse
Forgetting dx in trig substitution	After x = a sin(θ), dx must become a cos(θ) dθ, and the integral is missing a factor	Substitute x and dx together, every time
Wrong convergence test	A ratio test on a p-series is inconclusive and wastes time	Start with the nth term test, then recognize the series family
Absolute vs. conditional	An alternating series can converge while the series of absolute values diverges	Test both when the signs alternate
Skipping endpoints	The ratio test is inconclusive when the limit equals 1, so the open interval is incomplete	Test x = a − R and x = a + R separately (see the example above)
Disks vs. shells	Revolving about the x-axis, disks and washers integrate in x while shells integrate in y; mixing them gives a wrong setup	Sketch the region and the axis before choosing
Form of the answer	An auto-grader can reject an equivalent expression, a missing +C, or a decimal where exact form is expected	Read the entry instructions on each problem

Platforms

Your platform depends on your school and instructor. Each grades differently:

• MyLab Math: Pearson’s platform, often paired with Briggs and Cochran.
• WebAssign: Cengage’s platform, often paired with Stewart. Limited attempts and strict answer formatting.
• WileyPLUS: Wiley’s platform, often paired with Anton.
• ALEKS: McGraw Hill’s adaptive platform, with Knowledge Checks that can send learned topics back to your list.

Not sure which one your section uses? Tell us your school and instructor when you request a quote. Your syllabus and LMS login link will also say.

How We Help

Every assignment we complete is done by a human expert working inside your platform. Here’s why we use human experts instead of AI. In practice, that means:

• The integration technique chosen and shown, not just the final answer
• Convergence tests selected with the reasoning written out, and endpoints always checked
• Answer format matched to what each platform expects
• Help with quizzes, exams and full-course completion. For proctored exams, see our proctored exam help.

All work is covered by our A/B grade guarantee.

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MATH 2414 FAQ

Is MATH 2414 harder than MATH 2413?

Many students say yes. Calculus I rewards applying differentiation rules, while Calculus II asks you to recognize an integral’s form, pick a technique and choose the right convergence test for a series. Students who thrived on procedure sometimes struggle with that judgment, though students who already think in patterns may find the two comparable.

What’s the difference between MATH 2413, 2414 and 2415?

MATH 2413 is Calculus I, MATH 2414 is Calculus II (integration techniques, sequences and series, parametric and polar), and MATH 2415 is Calculus III (multivariable calculus). MATH 2415 is not Calculus II. Course numbers at individual schools can differ, so confirm equivalencies with your advisor before transferring.

What’s the prerequisite for MATH 2414?

Texas colleges generally require MATH 2413 (Calculus I) with a C or better. Some also set a time limit on how recently you took it, so check your college’s catalog.

Can AP Calculus BC replace MATH 2414?

Sometimes. AP Calculus BC covers material from both Calculus I and II, and many schools grant credit for a high enough score. The score you need and the courses you receive vary by school, so confirm with your registrar before relying on it.

What calculator do I need?

It depends on your instructor. Many courses allow a graphing calculator such as a TI-84, some prohibit calculators on exams to test conceptual understanding, and some ban symbolic (CAS) models like the TI-89 or TI-Nspire CAS. Check your syllabus.

Why does my platform mark a correct answer wrong?

Usually it’s the form: an equivalent expression the grader doesn’t recognize, a missing constant of integration, a decimal where exact form was expected, or an interval of convergence missing its endpoints. Read the entry instructions on each problem, and see the platform differences on our WebAssign and WileyPLUS pages.

Can you help with proctored MATH 2414 exams?

Yes. Proctoring rules are set by your school and instructor, so tell us the format and platform when you contact us. Details are on our proctored exam help page.

Do you guarantee grades?

Yes. Our A/B grade guarantee covers the work we complete. If we don’t deliver the agreed grade, you get a refund under the terms on that page.

Ready to Pass MATH 2414?

If integration techniques, convergence tests or your platform’s formatting rules are costing you points, we can take it from here. Get your free quote and we’ll reply with clear pricing, usually within hours.

Related Pages

• Texas Math Help
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