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3. Integrals
Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them. ∫ dx /x 2 ± a 2, ∫ dx /√x ^± a ^2 , ∫ dx /√a^ 2 − x^ 2 , ∫ dx /ax^2 + bx + c , ∫ (px + q /ax^2 + bx + c) dx, ∫ (px + q/ √ax2+bx + c) dx, ∫ (√a ^2 ± x^ 2) dx, ∫ √x ^2 − a^ 2 dx,
∫√????2 + ???????? + ???? ????????, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.