x-axis
Definition
The x-axis is the horizontal line on a coordinate plane that represents all possible x-values. It serves as reference for locating points in relation to their x-coordinates.
Analogy
Picture the x-axis as your street address line. Each point on this line has its unique address represented by its x-coordinate. Just like how addresses help locate places, the x-axis helps locate points on a coordinate plane.
Related terms
y-axis: The vertical line on a coordinate plane that represents all possible y-values.
Origin: The point (0, 0) where the x-axis and y-axis intersect on a coordinate plane.
Quadrants: The four regions formed by the intersection of the x-axis and y-axis on a coordinate plane.
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Practice Questions (9)
Consider a region defined by the function f(x) = x^3, revolved around the x-axis from x = 1 to x = 2. What is the volume of the solid formed by this revolution?
Consider a region defined by the function f(x) = x^2, revolved around the x-axis from x = 0 to x = 1. What is the volume of the solid formed by this revolution?
When revolving a region bounded by the graph of a function f(x) and the x-axis around the y-axis, what should be the limits of integration in the volume formula?
What is the volume of the solid obtained by rotating the region bounded by the curve y = x^3, the line y = 0, and the lines x = 1 and x = 2 around the x-axis?
What is the volume of the solid obtained by rotating the region bounded by the curves y = x² and y = 3x, and the line x = 0 around the x-axis?
Consider a region defined by the functions g(x) = x^3 and h(x) = 2x^3, revolved around the x-axis from x = 0 to x = 2. What is the volume of the resulting solid?
Which region is being revolved around the x-axis in the washer method?
Consider a region defined by the functions f(x) = 2x and h(x) = 3x, revolved around the x-axis from x = 0 to x = 2. What is the volume of the resulting solid?
Consider a region defined by the functions f(x) = x^2 and h(x) = 2x, revolved around the x-axis from x = 0 to x = 3. What is the volume of the resulting solid?
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