Integral Calculus
Calculus Contents F The indefinite integrals containing quadratic polynomial (trinomial) Recursion formulas - use of integration by parts formula
integration by parts formula examples Integrating rational functions
Use of the partial fraction decomposition to integrate a proper rational function
Use of the partial fraction decomposition to integrate a proper rational function examples
The Ostrogradsky method of the integration of a proper rational functions
The Ostrogradsky method of the integration of a proper rational functions examples Integrating irrational functions
Integration of irrational functions examples   Euler's substitutions
Integrating irrational functions using Euler's substitutions examples Binomial integral
Solving binomial integrals examples Trigonometric integrals
 Trigonometric integrals of the form ∫ sinm x, cosn x dx
Trigonometric integrals of the form
sin (m x) sin (n x) dx,    sin (m x) cos (n x) dx,    cos (m x) cos (n x) dx.
 Integrals of the rational functions containing sine and cosine, ∫ R (sin x, cos x) dx
Use of trigonometric identities and substitutions to solve trigonometric integrals Integrals of the hyperbolic functions Substitution and definite integration
Substitution and definite integration examples Integrations by parts and the definite integral The improper integrals Differentiation and integration of infinite series
Differentiation and integration of infinite series examples Differentiation and integration of power series
Applications of the definite integral The area of a region in the plane
The area between the graph of a curve and the coordinate axis
The area between the graph of a curve and the coordinate axis examples
The area bounded by a parametric curve
The area of the sector of a curve in polar coordinates
The area of the sector of a curve given in Cartesian (or rectangular) coordinates
The area of the sector of a parametric curve The area between two curves
The area between two curves examples Length of plane curve, arc length
Arc length of a parametric curve
Arc length of a curve in polar coordinates The volume of a solid of revolution
The volume of a sphere
The volume of a spherical segment
The volume of a cone The surface area of a solid of revolution
The lateral surface area of a cone
The surface area of a spherical cap
The surface area of an ellipsoid    