Set up the definite integral that gives the area of the region bounded by y = x^2 - 2x and the...

Question:

Set up the definite integral that gives the area of the region bounded by {eq}\displaystyle y=x^{2}-2x {/eq} and the {eq}x {/eq}-axis.

Definite Integrals; Geometric Applications:

We'll draw a diagram with the graph of the parabola {eq}y=x^{2}-2x {/eq} which will help us set up the definite integral to evaluate the area of the region bounded by it and the {eq}x {/eq}-axis. An important task is to determine the {eq}x {/eq} values of the points where parabola and the {eq}x {/eq}-axis intersect each other.

For {eq}x {/eq} in the interval {eq}[a,b] {/eq} we recall that the region has area {eq}A {/eq} given by:

{eq}A=\int_{a}^{b}(y_\text{top } )-(y_\text{bottom } )\,dx {/eq}

Answer and Explanation:

The diagram below presents portions of the graph of the parabola in blue color and the {eq}x {/eq}-axis in red color. We want to set up the definite...

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Calculating Integrals of Simple Shapes

from Math 104: Calculus

Chapter 13 / Lesson 1
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