NCERT Mathematics, Class 12, textbook pages 225–291 (Part II)

How to help your child with Class 12 Maths Chapter 7, Integrals, at home

Indefinite and definite integrals, explained for parents: a 60-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

∫ f(x) dx

NCERT Class 12 Maths Chapter 7 Integrals: what it teaches

Integration reverses differentiation. Your teen learns standard integrals, substitution, partial fractions and integration by parts, and evaluates definite integrals using the fundamental theorem.

Why it matters later. Integration is used for areas (Chapter 8), differential equations and physics.

See it: this chapter in pictures

∫2x cos(x²) dxu = x², du = 2x dx= sin(x²) + C
Spot the derivative inside.
∫x eˣ dxu = x (ILATE)= eˣ(x − 1) + C
Choose u wisely.
∫₀² x² dx= [x³/3]₀²= 8/3
Fundamental theorem.

You need

  • a formula sheet
  • practice problem set

Tonight’s 60 minutes

  1. Integrate x³ + 2x (x⁴/4 + x² + C).
  2. Use substitution for ∫2x cos(x²) dx (sin(x²) + C).
  3. Integrate by parts: ∫x eˣ dx (eˣ(x − 1) + C).
  4. Evaluate ∫₀² x² dx (8/3).

Words to use

  • antiderivative
  • constant of integration
  • substitution
  • by parts
  • partial fractions
  • definite integral

Watch for

  • Forgetting + C. Indefinite integrals always need a constant.
  • Choosing the wrong u in by parts. Use ILATE to pick u.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

You∫x eˣ dx: u = ?

Your childu = x by ILATE: eˣ(x − 1) + C.

A game for this week: Reverse it

  1. Write derivatives on cards.
  2. Players find the original function.
  3. Check by differentiating.
  4. Fastest wins.

A 5-day plan, 60 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Area and volume.
  • Distance from velocity.
  • Work in physics.
  • Probability.

Quick check

Ask these at the end of the week. Tap to see the answer.

∫x³ dx?

x⁴/4 + C.

∫x eˣ dx?

eˣ(x − 1) + C.

∫₀² x² dx?

8/3.

Ready for the next chapter when your child…

  • Knows standard integrals.
  • Uses substitution, by parts and partial fractions.
  • Evaluates definite integrals.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 12). See the full Class 12 parent guide for every chapter.

Questions parents ask

Why add + C?

Many functions share the same derivative.

What is ILATE?

A priority order for choosing u in integration by parts.

What is the fundamental theorem?

∫ₐᵇ f(x) dx = F(b) − F(a).