Class 12 Mathematics Chapter 8 Applications of Integrals – Revision Notes

Quick revision notes for Class 12 Maths Chapter 8 (Applications of Integrals). These Class 12 Mathematics Chapter 8 notes are ideal for quick revision just before exams.

Area Formulas

• Under curve: ∫_a^b|f(x)|dx.
• Between curves: ∫_a^b[f(x)−g(x)]dx (upper−lower).
• Circle x²+y²=a²: area=πa².

Method

• Sketch curves, find intersection points as limits.
• Integrate w.r.t. y when region is naturally x=g(y).
• Split composite regions into simpler sub-integrals when needed.

One-Line Summary

Applications of Integrals uses definite integrals to compute areas under and between curves, requiring careful sketching to identify limits and which curve bounds the region above/below.

Written by Satish

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