Integration reverses differentiation and adds up quantities. This course covers every standard method of integration and the properties of definite integrals.
The course follows the NCERT Class 12 Mathematics chapter Integrals and has 3 lessons. Each lesson explains the ideas with worked examples and ends with practice questions and full answers. The numbers in every example and question are our own, so the lessons can be used alongside the textbook exercises.
- Indefinite Integrals and Substitution — Antiderivatives, standard integrals, substitution, and integrals using trigonometric identities.
- Special Forms, Partial Fractions and Integration by Parts — Standard forms with x squared plus or minus a squared, partial fractions, integration by parts and the e to the x form.
- Definite Integrals and Mixed Practice — The fundamental theorem of calculus, substitution in definite integrals, properties of definite integrals, and mixed practice.
By the end you will be able to:
- Integrate using standard results and substitution.
- Use partial fractions and special forms.
- Integrate by parts.
- Evaluate definite integrals using their properties.