Net signed area

Definition

Net signed area is the total area between a curve and the x-axis, accounting for areas where the curve is below the x-axis as negative. It is computed using definite integrals and can result in a positive, negative, or zero value.

5 Must Know Facts For Your Next Test

1. Net signed area is calculated using the definite integral of a function over a specified interval.
2. When a curve lies above the x-axis, its contribution to the net signed area is positive; when it lies below, its contribution is negative.
3. If a function crosses the x-axis within the integration bounds, you need to split the integral at the points where it crosses.
4. The net signed area gives insight into both magnitude and direction of accumulated quantities.
5. In application problems, net signed areas can represent quantities such as displacement (considering direction) versus total distance traveled.

Review Questions

• How does one compute net signed area using definite integrals?
• What does it mean when part of the graph of a function lies below the x-axis?
• Why might you need to split an integral at certain points when calculating net signed area?

Related terms

Definite Integral: A mathematical expression representing the accumulation of quantities and computed as the limit of Riemann sums over an interval.

Riemann Sum: An approximation of an integral by summing up areas of rectangles or trapezoids under a curve.

Antiderivative: A function whose derivative is equal to the given function; used in finding definite integrals through the Fundamental Theorem of Calculus.