Integration (Calculus): JAMB Mathematics Questions, Answers & Notes

What Integration (Calculus) covers in the JAMB Mathematics syllabus

Calculus has two halves. Differentiation finds the gradient (rate of change): for y = xⁿ, dy/dx = nxⁿ⁻¹; the derivative of a constant is 0. Differentiate term by term. The gradient at a point comes from substituting the x-value into dy/dx, and at a turning point (max/min) dy/dx = 0. Integration is the reverse: ∫xⁿ dx = xⁿ⁺¹/(n+1) + c (don't forget +c for indefinite integrals). A definite integral ∫ₐᵇ evaluates the antiderivative at the limits and subtracts, giving the area under the curve. In motion, velocity = ds/dt and acceleration = dv/dt.

For Integration (Calculus), JAMB expects you to be able to:

• Differentiate polynomial functions and find gradients and turning points
• Integrate polynomial functions, including definite integrals
• Apply calculus to rates of change and area under a curve

Key facts & revision notes: Integration (Calculus)

These are the recurring points our Integration (Calculus) questions test — revise them until each feels automatic, then practise the questions above to lock them in.

• Bring the power down and reduce it by 1: dy/dx = 3x².
• Differentiate term by term: d(5x²)=10x, d(2x)=2, so dy/dx = 10x + 2.
• The derivative of any constant is 0.
• Increase the power by 1 and divide: ∫2x dx = 2·x²/2 + c = x² + c.
• ∫xⁿ dx = xⁿ⁺¹/(n+1) + c, so ∫x² dx = x³/3 + c.
• dy/dx = 4 × 5 × x⁴ = 20x⁴.
• At x = 3, gradient = 2 × 3 = 6.
• ∫6x² dx = 6·x³/3 + c = 2x³ + c.
• Differentiate term by term: 2x − 4 + 0 = 2x − 4.
• First derivative 3x²; differentiate again to get 6x.
• At a maximum or minimum (turning point), the gradient dy/dx = 0.
• ∫2x dx = x²; evaluate from 0 to 1: 1² − 0² = 1.
• d(3x⁴)=12x³, d(−2x²)=−4x, so dy/dx = 12x³ − 4x.
• ∫3x² dx = x³ and ∫1 dx = x, so the integral is x³ + x + c.
• The derivative of distance with respect to time is velocity.
• At t = 1, velocity = 6 + 2 = 8.
• The derivative of 7x is 7 (the coefficient).
• A definite integral gives the area under a curve between the limits.
• Using (0,3): 3 = 0 + c so c = 3, giving y = x² + 3.
• d/dx(xⁿ) = nxⁿ⁻¹, so 4x³.
• Differentiate term by term: 6x + 4.
• The derivative of a constant is 0.
• ∫4x dx = 4·x²/2 + C = 2x² + C.
• ∫xⁿ dx = xⁿ⁺¹/(n+1) + C = x⁶/6 + C.

Worked examples

Three Integration (Calculus) questions with the answer and a short explanation, so you can see how the topic is set before you practise the full set.

How Integration (Calculus) is tested in JAMB Mathematics

Our Integration (Calculus) bank holds 40 questions (12 easy, 20 medium, 8 hard). JAMB Mathematics typically returns to Integration (Calculus) year after year, so steady practice on this topic is high-value revision. Questions are multiple-choice with four options, and at UTME pace you get roughly 40 seconds each — which is why timed practice matters.

How to answer Integration (Calculus) questions

Work the stem first and predict the answer before you look at the options; then eliminate the ones that contradict the key facts above. Watch for “which is not…”, “all of the above” and “except” style stems, which are where rushed candidates lose easy marks on Integration (Calculus). If a calculation or a precise definition is involved, work it from first principles rather than guessing from a half-remembered rule. When two options look right, re-read the stem for the qualifier that separates them — JAMB rarely repeats an option by accident. If you are still unsure, eliminate the two weakest choices to lift your odds, flag the question, and move on; never burn a full minute on one Mathematics item when the exam gives you about forty seconds each. Then come back to flagged questions with whatever time remains. The single most reliable way to get faster at Integration (Calculus) is repeated timed practice, so use the button above until the recurring patterns feel automatic.

Common mistakes to avoid in Integration (Calculus)

The errors that cost marks on Integration (Calculus) are usually careless rather than conceptual: misreading a negative stem, confusing two similar terms, or rushing a definition you actually know. Candidates also over-rely on “expo” and last-minute cramming instead of understanding the topic — which fails the moment JAMB rephrases a familiar idea. Treat every option as a claim to be checked against the facts above, keep your working tidy for any calculation, and don’t change a considered answer on a hunch. Above all, revise Integration (Calculus) actively by answering questions, not just by re-reading notes — recall under time is what the exam rewards.

Frequently asked questions

Is Integration (Calculus) part of the JAMB Mathematics syllabus?

Yes. Integration (Calculus) is a recognised topic in the JAMB Mathematics syllabus, covering differentiate polynomial functions and find gradients and turning points. You should be able to recall its key facts and apply them to multiple-choice questions.

How many Integration (Calculus) questions can I practise on Belmadeng?

There are 40 original, JAMB-standard Integration (Calculus) questions in our free bank, each with the correct answer and a worked explanation. You can practise them untimed or as a timed test.

What are the most important points to know about Integration (Calculus)?

Calculus has two halves. Differentiation finds the gradient (rate of change): for y = xⁿ, dy/dx = nxⁿ⁻¹; the derivative of a constant is 0. Differentiate term by term. The gradient at a point comes from substituting the x-value into dy/dx, and at a turning point (max/min) dy/dx = 0. Integration is t…

How do I answer Integration (Calculus) questions quickly in JAMB?

Read the stem carefully, eliminate clearly wrong options, and match the remaining choices to the key facts for Integration (Calculus). Practising timed Integration (Calculus) questions builds the speed you need for UTME's pace of about 40 seconds per question.

Are these JAMB Mathematics Integration (Calculus) questions past questions or original?

They are original questions written to JAMB (UTME) standard and mapped to the official syllabus — not reproduced past papers. This keeps them legal to use freely while closely mirroring how the real exam tests the topic.

Where can I practise Integration (Calculus) questions free without signing up?

Right here — tap “Start Integration (Calculus) practice” on this page to begin instantly. Belmadeng's CBT practice is completely free and needs no sign-up, download or subscription.

About these questions: original, JAMB-standard items written from the official UTME Mathematics syllabus (last reviewed 2026-09-18). Belmadeng is an independent study platform and is not affiliated with JAMB. Spotted an error? Use the report link.