Step Function Integral Calculator
Integration Results
Definite Integral: -
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Understanding Step Functions and Integration
What is a Step Function?
A step function is a piecewise constant function that takes only a finite number of values.
Key Concepts:
∫f(x)dx = Σ(height × width) for each step
Area = |∫f(x)dx|
Properties:
- Discontinuous at jump points
- Constant between jumps
- Right/left continuous
- Bounded and measurable
Integration Methods
- Riemann Sum Approach
- Left/Right-hand Evaluation
- Midpoint Method
- Lebesgue Integration
- Simple Function Approximation
- Partition Refinement
Applications
Signal Processing
Digital signals analysis
Economics
Supply/demand models
Control Theory
Switching systems
Probability
Cumulative distribution
Advanced Properties
- Measurability: Always Lebesgue measurable
- Integrability: Always Riemann integrable
- Convergence: Pointwise vs. uniform
- Density: Dense in L¹ spaces
- Approximation: Simple function theorem
- Regularity: Regulated functions