JEE Integration Quiz
Practice on standard integrals, substitution, integration by parts and partial fractions, the properties of definite integrals, and area under curves.
Skill map
Levels in this jee integration quiz
Every question is generated fresh by AI and calibrated to your level - clear a level and the next one gets harder. Miss one and the AI tutor explains Integration until it sticks, then aims a follow-up at the gap. Want to grind one level? Start the quiz and type that sub-topic as your own.
Exam focus
How Integration is asked
Consistently one of the largest contributors in JEE Mathematics, and the chapter where technique selection decides speed. The properties of definite integrals in particular can collapse an apparently impossible integral into a one-line answer, and JEE sets questions specifically to reward knowing them.
Cheat sheet
Integration formulas worth memorising
| Quantity | Formula |
|---|---|
| Power rule | ∫xⁿ dx = x^(n+1)/(n + 1) + C, n ≠ −1 |
| Reciprocal | ∫(1/x) dx = ln|x| + C |
| Integration by parts | ∫u dv = uv − ∫v du (choose u by ILATE) |
| Definite integral property | ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a − x)dx |
| Odd/even property | ∫₋ₐᵃ f = 0 if f odd, 2∫₀ᵃ f if f even |
| Area between curves | ∫ (upper − lower) dx |
| Fundamental theorem | ∫ₐᵇ f(x)dx = F(b) − F(a) |
Marks lost here
Common mistakes in Integration
- Forgetting the constant of integration on indefinite integrals. It is a standard mark deduction and, in differential-equation questions, it is the whole answer.
- Not changing the limits after substitution in a definite integral. Either convert the limits to the new variable or substitute back before evaluating - mixing the two silently gives a wrong value.
- Choosing u badly in integration by parts. ILATE - inverse, logarithmic, algebraic, trigonometric, exponential - gives the priority order, and picking the wrong u often makes the integral harder rather than easier.
- Computing the area under a curve as a plain definite integral when the curve crosses the axis. Below the axis the integral is negative, so area needs the region split at the crossing points and the magnitudes added.
- Applying ∫xⁿ dx = x^(n+1)/(n+1) at n = −1. That case gives ln|x|, and the absolute value matters for negative x.
Game rules
How a round works
- 01Spawn
Press play - the AI generates Integration questions in seconds.
- 02Level up
Answer to earn XP and build a streak. Difficulty adapts to your accuracy and speed.
- 03Learn or lose
Every answer - right or wrong - gets an AI tutor explanation. Wrong answers respawn as follow-ups.
Leaderboard
Integration high scores
Next challenges
Related quizzes to conquer
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▶Chapter-wise practice on the rules of differentiation, chain rule, implicit and parametric differentiation, and applications to tangents, maxima and minima.
JEE Limits Quiz
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JEE Probability Quiz
▶Chapter-wise practice on classical probability, addition and multiplication rules, conditional probability, Bayes' theorem and the binomial distribution.
JEE Maths Quiz
▶JEE Mathematics MCQs on calculus, algebra, coordinate geometry, trigonometry, vectors and probability - the scoring subject when practiced right.
Player's guide
JEE Integration Quiz - FAQs
Which definite-integral property is most useful in JEE?
∫₀ᵃ f(x)dx = ∫₀ᵃ f(a − x)dx. Adding the original integral to its transformed version frequently cancels the difficult part entirely, turning an intractable integrand into a constant. Questions are constructed around this deliberately.
How do I choose between substitution and integration by parts?
Use substitution when the integrand contains a function and something proportional to its derivative. Use parts when it is a product of two unrelated function types, such as an algebraic term times an exponential or a logarithm - ILATE then tells you which factor to differentiate.
Is the jee integration quiz free?
Yes - completely free, with no sign-up required. Type a topic, press start, and the AI generates an adaptive Integration quiz with an explanation for every answer.
Can teachers host this jee integration quiz live for a class?
Yes - create a free teacher account, host a live room on "Integration", and students join with a 6-character code at quff.in/join. No student accounts needed.
From the blog
Integration guides & reading
JEE Integration: 30 Practice Questions with Solutions
Thirty solved Integration questions, organised around the only decision that matters: which technique the integrand is asking for.
Exam PrepJEE Limits: 30 Practice Questions with Full Solutions
Thirty solved Limits questions, starting from the check that decides the method: is the form actually indeterminate?
Exam PrepJEE Differentiation: 30 Practice Questions with Solutions
Thirty solved Differentiation questions, weighted toward applications of derivatives - which is where the paper actually puts its marks.
More exam prep quizzes
Ready, player?
Six adaptive Integration questions. About two minutes. Climb the podium.