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131
Trigonometric integrals
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Trigonometric
integrals of the form
A
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Evaluating
trigonometric
integrals using substitutions examples
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132
Evaluating
trigonometric
integrals using substitutions and trigonometric identities examples
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Evaluating
trigonometric
integrals using substitution tan x = t
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Trigonometric
integrals of the form B
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133
Integrals
of rational functions containing sine and cosine
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Integrals
of rational functions containing sine and cosine examples
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Integrals
of the hyperbolic functions
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Integrals
of the hyperbolic functions examples
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134
Substitution
and definite integration
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Substitution
and definite integration examples
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Integrations
by parts and the definite integral
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The
improper integrals
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The
improper integrals examples
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135
Differentiation
and integration of infinite series
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Differentiation
and integration of infinite series examples
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Differentiation
and integration
of power series
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Representing
the integrand function as the power series
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136
Applications
of the definite integral
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The
area of a region in the plane
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The
area between the graph of f(x) and the x-axis
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The
area between the graph of a curve and the coordinate axis examples
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The
area bounded by a parametric curve
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137
The
area of the sector of a curve in polar coordinates
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The
area of the sector of a curve given in Cartesian (or rectangular) coordinates
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The
area of the sector of a parametric curve
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The
area between two curves
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The
area between two curves examples
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138
Length of plane curve, arc length
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Length
of plane curve
given in Cartesian (or rectangular) coordinates
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Arc length of a parametric curve
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Arc length of a curve in polar coordinates
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139
The
volume
of a solid of revolution
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The
volume
of a sphere
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The
volume
of a spherical segment
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The
volume
of a cone
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The
volume
of a solid of revolution examples
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140
The
surface area of a solid of revolution
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The
surface area generated by rotating a parametric curve
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The
lateral surface area of a cone
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The surface area of a spherical
cap
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The surface area of an
ellipsoid
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