Class XII Mathematics
Chapter 6: Integrals
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Syllabus Sections
Key Formulas & Equations
Click Copy to duplicateIntegration by Parts
\int u v \, dx = u \int v \, dx - \int (u' \int v \, dx) \, dx
Rule for integrating product of two functions.
Definite Integral Fundamental Theorem
\int_{a}^{b} f(x) \, dx = F(b) - F(a)
Relates definite integral to antiderivative values.
Related Formulas from Adjacent Chapters
Power Rule of Differentiation
\frac{d}{dx}(x^n) = n x^{n-1}
[From Continuity and Differentiability] Differentiates exponential variable functions.
The Chain Rule
\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}
[From Continuity and Differentiability] Differentiates nested composite functions.
Area Bounded by Curve
Area = \int_{a}^{b} f(x) \, dx
[From Application of Integrals] Calculates area under curve y = f(x) from x = a to x = b.