Average of an Integral
For f (x) continuous in the interval I = [a,b] where a < b, the average value of f (x) in I equals:
Example:
Find the average value of the function f (x) = x2 + 1 in the interval I = [0,4]
Solution:
- Limits
- l'Hopital's Rule
- Squeeze Theorem for Limits
- Limits of Composite Functions
- Derivative
- Continuity & Differentiability
- Mean Value Theorem
- Derivatives: Product Rule
- Derivatives: Quotient Rule
- Derivatives: Chain Rule
- Derivatives of Inverse Functions
- Linear Approximation
- Higher-Order Derivatives
- 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)
