Integral Calculus
Calculus Contents F
The indefinite integrals
c)
Types of the indefinite integrals
The indefinite integrals containing quadratic polynomial (trinomial)
The indefinite integrals containing quadratic polynomial examples
Recursion formulas - use of
integration by parts formula
Recursion formulas - use of
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
Integration of irrational functions of the form
Integration of irrational functions of the form
Integrals of the form
Euler's substitutions
Integrating irrational functions using Euler's substitutions examples
Binomial integral
Solving binomial integrals examples
Trigonometric integrals
Trigonometric integrals of the form
∫
sin
m
x
, cos
n
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
The improper integral definition
The improper integrals examples
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
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