Class 12 Mathematics Chapter 7 Integrals – Revision Notes

Quick revision notes for Class 12 Maths Chapter 7 (Integrals). These Class 12 Mathematics Chapter 7 notes are ideal for quick revision just before exams.

Standard Integrals

• ∫xⁿdx=xⁿ⁺¹/(n+1)+C; ∫1/x dx=log|x|+C; ∫e^xdx=e^x+C.
• ∫sin x dx=−cos x+C; ∫cos x dx=sin x+C.

Techniques

• Substitution, partial fractions, integration by parts (∫u dv=uv−∫v du, ILATE order).

Definite Integrals

• ∫_a^bf(x)dx=F(b)−F(a) (Fundamental Theorem).
• Key property: ∫_a^bf(x)dx=∫_a^bf(a+b−x)dx.

One-Line Summary

Integration reverses differentiation; indefinite integrals carry a constant C, while definite integrals compute exact signed area using the Fundamental Theorem of Calculus and simplifying properties.

Written by Satish

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