Area under the curve
Definition
The area under the curve refers to the total amount of space enclosed between a function and the x-axis on a given interval.
Analogy
Imagine you have a piece of land with different elevations. The area under the curve is like calculating the total amount of land you own by measuring all the space within your property boundaries.
Related terms
Riemann Sum: A method used to approximate the area under a curve by dividing it into smaller rectangles and summing their areas.
Definite Integral: A mathematical operation that calculates the exact value of the area under a curve between two specific points.
Trapezoidal Rule: An approximation technique for finding the area under a curve by dividing it into trapezoids and summing their areas.
"Area under the curve" appears in:
Study guides (1)
Practice Questions (7)
- What does the area under the curve of a non-negative function represent?
- What does the area under the curve of a negative function represent?
- What does the area under the curve of a decreasing function represent?
- What does the area under the curve of a constant function represent?
- What does the area under the curve of an increasing function represent?
- What is the area under the curve y = x² from x = 0 to x = 2?
- What is the method used to calculate the area under the curve for polar functions?
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