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Mathematics - Calculus: Differentiation and Integration (Form V & VI)
Muhtasari / Summary: Differentiation rules, integration, and applications of calculus.
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Calculus is the study of rates of change and accumulation. Differentiation: dy/dx measures the gradient (rate of change). Rules: Power rule – d/dx(xⁿ) = nxⁿ⁻¹; Product rule; Chain rule. Integration (reverse of differentiation): ∫xⁿ dx = xⁿ⁺¹/(n+1) + C. Definite integrals calculate area under a curve: ∫ₐᵇ f(x) dx. Applications: finding maxima/minima (set dy/dx=0), velocity, acceleration, areas, and volumes. Developed independently by Newton and Leibniz.