Indefinite Integration: Substitution & Integration by Parts Study Guide: NEB 11 Maths

Seven-session plan

Turn Indefinite Integration: Substitution and Integration by Parts into retrievable knowledge

Indefinite integration finds families of antiderivatives. Substitution reverses the chain rule, while integration by parts reverses the product rule; both require a final constant of integration.

1. Map prerequisites and definitions.
2. Derive or justify the main relation: ∫f(g(x))g′(x)dx=∫f(u)du and ∫u dv=uv−∫v du.
3. Redraw diagrams from memory.
4. Study this worked checkpoint: ∫2x cos(x²)dx=sin(x²)+C by u=x². Also ∫x e^x dx=x e^x−e^x+C.
5. Mix conceptual and numerical questions.
6. Complete a timed closed-book set.
7. Retest only the first wrong decision in each answer.

Use contrast tables and error cards

Place easily confused ideas side by side. Write what stays fixed, what changes, the governing equation and the observable consequence. One high-value warning is: Omitting +C, changing variables without transforming dx, choosing parts that make the integral harder, or differentiating the final answer incompletely.

Use spaced retrieval: ten minutes today, a closed-book test tomorrow and a mixed review after one week. Explain every graph or diagram aloud before using algebra.

NEB answer method

Model → evidence → equation → check

First identify the system and what the question asks. Label the diagram, apparatus or reaction with SI quantities, then state the principle before selecting an equation. Solve symbolically where possible and check units, limiting cases and chemical or physical meaning.

Make the idea concrete in Nepal

Connect the model to a school laboratory, household technology, health, environment, energy or local material. The example should clarify the science rather than merely mention a place. Compare a prediction with an observation and record uncertainty.

Review the NEB Class 11 Mathematics revision roadmap and the complete Mathematics guide. For online or physical tuition, call 9846662070.

Frequently asked questions

Questions students ask about Indefinite Integration: Substitution and Integration by Parts

References and next steps

Scope checked against CDC Nepal; concept support from an institutional reference and OpenStax Science. Continue with the Indefinite Integration: Substitution and Integration by Parts cluster.