CBSE · Class 6-12

Class 12 · Mathematics (041)

Unit 7 · Class 12Mathematics (041)

Calculus

Integrals

Indefinite and definite integrals, standard forms, substitution, by parts, partial fractions.

Lessons

5 concepts

1
Indefinite Integrals
$\int f(x)\, dx = F(x) + C$ where $F' = f$ .
2
Standard Integrals
$\int x^n dx = \dfrac{x^{n+1}}{n+1} + C$ (for $n \ne -1$ ); $\int \dfrac{1}{x} dx = \ln|x| + C$ .
3
Substitution
$\int f(g(x)) g'(x) dx = \int f(u) du$ where $u = g(x)$ .
4
Integration by Parts
$\int u\, dv = uv - \int v\, du$ .
5
Definite Integrals
$\int_a^b f(x) dx = F(b) - F(a)$ . Properties: $\int_a^b = -\int_b^a$ ; $\int_a^b = \int_a^c + \int_c^b$ .

Skills to practise

Skill · medium

Integrals — Practice (coming soon)

Practice bank for this unit is in progress. You can still read the lessons above.