Class 12 Integration

Evaluate integrals of products using integration by parts, selecting the differentiated factor through structural reasoning.

Evaluate rational-function integrals using polynomial division and partial-fraction decomposition.

Transform and evaluate trigonometric integrals by selecting identities and substitutions according to the powers and forms present.

Evaluate definite integrals using the Fundamental Theorem of Calculus, including changing limits during substitution.

Simplify definite integrals using interval reversal, interval splitting, symmetry, and periodicity properties.

Formulate and evaluate definite integrals for areas under curves and between curves, splitting intervals when signs or curve order change.