Chapter test · Mathematics · Class 12

Integral Calculus

This test asks up to 25 questions on the real pattern and marking, and hands you a concept-by-concept report the moment you finish. It covers 3 key concepts: Indefinite integration techniques, Definite integrals and properties and Area under curves.

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Questions

Up to 25 — 20 MCQ + 5 numerical

Time

60 minutes, fixed

Marking

JEE Main: +4 / −1 on A, +4 / 0 on B

Class

Class 12 · Mathematics

Report

Concept breakdown + cognitive demand, instantly

What this test covers

3 key concepts, tested the way the exam tests them.

Mapped from EduPeak’s learning framework for this chapter — the same map your report scores you against.

1
Indefinite integration techniques
- Integrates using substitution, parts and partial fractions with standard forms.Apply & Analyse
2
Definite integrals and properties
- Evaluates definite integrals using fundamental theorem and symmetry/King properties.Apply & Analyse
3
Area under curves
- Computes areas bounded by curves and lines using definite integrals.Apply & Analyse

Level of thinking demanded3 learning objectives

Recall & understandingApply & AnalyseHigher-order

This chapter is tested mostly at the Apply & Analyse level.

In your board

Where this chapter sits in your syllabus.

The same EduPeak test, found under your own textbook’s chapter name.

CBSE
Integrals · Application of Integrals
✓ in your syllabus
Gujarat (GSEB)
Integrals · Application of Integrals
✓ in your syllabus
Madhya Pradesh (MPBSE)
Integrals · Application of Integrals
✓ in your syllabus
Rajasthan (RBSE)
Integrals · Application of Integrals
✓ in your syllabus
Bihar (BSEB)
Unit-III Calculus — Indefinite Integrals · Unit-III Calculus — Definite Integrals · Unit-III Calculus — Application of the Integrals
✓ in your syllabus
Uttar Pradesh (UPMSP)
कलन - समाकलन / Integrals · कलन - समाकलनों के अनुप्रयोग तथा अवकल समीकरण / Applications of Integrals and Differential Equations
✓ in your syllabus
ISC (CISCE)
Calculus - Integrals · Calculus - Application of Integrals
✓ in your syllabus
Cambridge International A Level
Integration (P1 · P3)
✓ in your syllabus
IB Diploma Programme (HL)
SL 5.5 Introduction to integration as anti-differentiation (Topic 5: Calculus) · SL 5.10 Indefinite integral of x^n, sin, cos, 1/x, e^x (Topic 5: Calculus) · SL 5.11 Definite integrals; area between a curve and the x-axis (Topic 5: Calculus) · AHL 5.16 Integration by substitution and by parts (Topic 5: Calculus) · AHL 5.17 Area between curves; volumes of revolution (Topic 5: Calculus)
✓ in your syllabus

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Try one

A sample question from this chapter.

Drawn fresh from the chapter’s bank on every visit. Reveal the worked solution when you are ready — the way your report explains every question.

SampleMathematics· MCQ+4 / -1

Let

f : R \to R

be a function defined by

f (x) = \frac{x}{( 1 + x ^{4} ) ^{1/4}}

, and

g (x) = f (f (f (f (x))))

. Then

18 \int_{0}^{52} x^{2} g (x) d x

is equal to

A. $33$
B. $39$
C. $36$
D. $42$

Worked, step by step — the way your report explains every question. Loads on request.

In the real test, every question is fresh from the chapter’s bank — and your report shows the worked solution for each one.

Keep climbing

Related Class 12 Mathematics chapters

Sets, Relations and Functions Matrices and Determinants Limits, Continuity and Differentiability Differential Equations Three Dimensional Geometry Vector Algebra

Good to know

About this chapter test

How is the test scored?

Exactly like JEE Main: +4 for a correct answer, −1 for a wrong MCQ, and no negative marking on numericals. Your total, pacing and concept-by-concept accuracy appear in your report the moment you submit.

Which class is Integral Calculus in?

Integral Calculus sits in Class 12 Mathematics here. Pick your class when you start — the whole chapter list is organised the same way.

Can I take it more than once?

Yes — each attempt draws from the chapter’s bank, and your report tracks your best and your progress across attempts.

Is it free?

Free chapter tests are included with every account, and each one comes with the complete report. No card needed to start.

25 questions. 60 minutes. One honest answer.

Find out exactly where you stand on this chapter — today.

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