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Integrals: Volume by Cylindrical Shells
Limits
l'Hopital's Rule
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Applications of Differentiation: Critical Points
Applications of Differentiation: Second Derivative Test
Partial Derivatives
Integral
Average of an Integral
Integration by Parts
Improper Integrals
Integrals: Area Between Curves
Integrals: Volume by Cylindrical Disks
Integrals: Volume by Cylindrical Shells
Integrals: Length of a Curve
Integrals: Work as an Integral
Numerical Integration: Trapezoidal Rule
Numerical Integration: Simpson's Rule
Hyperbolic Functions
Inverse Hyperbolic Functions
Infinite Series: Geometric Series
Infinite Series: P-series
Infinite Series: Harmonic Series
Infinite Series: Integral Test For Convergence
Infinite Series: Ratio Test For Convergence
Infinite Series: Root Test For Convergence
Taylor's Formula
Integrals: Length in Polar Coordinates
Integrals: Area in Polar Coordinates
Dot Product of Vectors
Curvature For Parametric Plane Curves
Curvature For Non-Parametric Plane Curves
Cross Product of Vectors
Quadric Surfaces
Directional Derivative
Double Integrals: Iterated Integrals
Double Integrals: Properties
Double Integrals: Surface Area
Triple Integrals
Gradient of a Scalar Function
Line Integral of a Vector Field
Line Integral of a Scalar Field
Green's Theorem
Divergence of a Vector Field
Curl of a Vector Field
List of Derivatives of Simple Functions
List of Derivatives of Log and Exponential Functions
List of Derivatives of Trig & Inverse Trig Functions
List of Derivatives of Hyperbolic & Inverse Hyperbolic Functions
List of Integrals Containing cos
List of Integrals Containing sin
List of Integrals Containing cot
List of Integrals Containing tan
List of Integrals Containing sec
List of Integrals Containing csc
List of Integrals of Inverse Trig Functions
List of Integrals of Hyperbolic Functions
List of Integrals of Inverse Hyperbolic Functions
List of Integrals of Rational Functions
List of Integrals Containing ln
List of Integrals Containing exp(x)
Integrals: Volume by Cylindrical Shells
Let
f
(
x
) be continuous and nonnegative in [
a,b
] where
a
≥ 0. When the region under the graph
y
=
f
(
x
),
a
≤
x
≤
b
, is rotated about the
y
axis, a solid of revolution is generated whose volume is
Related Topic:
Volume by Cylindrical Disks