Net signed area

Definition

Net signed area is the total area calculated by taking into account the direction (positive or negative) above and below the x-axis for a given function over a specific interval. It represents the integral of a function, considering both positive and negative contributions.

5 Must Know Facts For Your Next Test

1. Net signed area can be computed using the definite integral of a function over an interval $[a, b]$.
2. If a function is above the x-axis, its contribution to net signed area is positive; if below, its contribution is negative.
3. The net signed area may be zero if areas above and below the x-axis cancel out each other.
4. It differs from total area in that it accounts for sign changes when crossing the x-axis.
5. Net signed area can be visualized as the algebraic sum of areas between the curve and the x-axis.

Review Questions

• What does it mean for an integral to have a net signed area?
• How does net signed area differ from total area?
• Why might a net signed area be zero even if there are regions where the function has non-zero values?

Related terms

Definite Integral: The evaluation of the integral of a function over a specific interval $[a, b]$, representing net signed area.

Total Area: The absolute value of all areas between a curve and the x-axis over an interval without considering sign.

Fundamental Theorem of Calculus: A principle that links differentiation and integration, stating that differentiation undoes integration and vice versa.