Finding the Area of a RegionIn Exercises 7–10, use an iterated integral to find the area of the region bounded by the graphs of the equations.
To calculate: The area of the region bounded by the graphs of given equation , , and .
Given: The provided equations are:
, , and
Formula used: The area of a region is given by
Vertex form of parabola’s equation is given by
Here is the vertex of the parabola
Calculation: The equation is the equation of a parabola.
Write it in its vertex form
Vertex of this parabola is given by
The equation represents y-axis.
The equation represents x-axis.
The equation is a straight line parallel to x-axis passing through .
Intersection of parabola and line is:
Therefore, the intersection point is
Calculus: Early Transcendental Functions
Precalculus: Mathematics for Calculus (Standalone Book)
Finite Mathematics and Applied Calculus (MindTap Course List)
Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals, Volume I
Calculus: An Applied Approach (MindTap Course List)
Essentials Of Statistics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Calculus (MindTap Course List)
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Statistics for The Behavioral Sciences (MindTap Course List)
Understanding Basic Statistics
Single Variable Calculus
Mathematical Excursions (MindTap Course List)
Mathematical Applications for the Management, Life, and Social Sciences
Probability and Statistics for Engineering and the Sciences
Single Variable Calculus: Early Transcendentals
Trigonometry (MindTap Course List)
Elementary Technical Mathematics
Contemporary Mathematics for Business & Consumers
Elementary Geometry For College Students, 7e
Elements Of Modern Algebra
Calculus: Early Transcendental Functions (MindTap Course List)
Calculus of a Single Variable
Elementary Geometry for College Students
Finite Mathematics for the Managerial, Life, and Social Sciences