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JEE Main Mathematics

Definite Integrals & Properties

No official chapter weightage

King's property (f(a+b-x)), Leibniz derivative rule for integral bounds, and area bounded by curves.

∫abf(x) dx=∫abf(a+b−x) dx,ddx∫ϕ(x)ψ(x)f(t)dt=f(ψ)ψ′−f(ϕ)ϕ′\int_{a}^{b} f(x)\,dx = \int_{a}^{b} f(a+b-x)\,dx, \quad \frac{d}{dx}\int_{\phi(x)}^{\psi(x)} f(t)dt = f(\psi)\psi' - f(\phi)\phi'

What this unit covers

  • King's Property & Symmetrical Simplification

  • Leibniz Differentiation Under Integral Sign

  • Definite Integral as Limit of a Riemann Sum

  • Area Under Curves & Intersection Bounds

Other units in JEE Main Mathematics