Integrals — Class 12 Mathematics

Integration is the inverse process of differentiation. The indefinite integral gives the family of antiderivatives of . This chapter builds a toolkit of methods: integration by substitution, integration using partial fractions, and integration by parts, . Standard forms for integrals of trigonometric, exponential and rational functions are tabulated. The definite integral is introduced as a limit of sums and evaluated using the Fundamental Theorem of Calculus, , where . Properties of definite integrals — additivity over intervals, symmetry over , and the king's rule — simplify many evaluations.