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intenzxboi
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Homework Statement
Find area between
f(x) = 1 / 1+x^2 and the line y= 1/2
The Attempt at a Solution
would i need to take the anti derivative of it then minus 1/2??
The process for finding the area between a graph and the x-axis is to first identify the points where the graph intersects the x-axis. Then, draw vertical lines from those points to the x-axis. This creates a series of rectangles. Finally, calculate the area of each rectangle and add them together to find the total area between the graph and the x-axis.
No, the area between a graph and the x-axis cannot be negative. The area represents a physical quantity and cannot have a negative value. If the graph dips below the x-axis, the area between the graph and the x-axis is calculated as a negative value, but the actual area is positive.
If the graph is not a straight line, the area between the graph and the x-axis can still be calculated using the same process. However, instead of rectangles, the area will be made up of smaller, more complex shapes. The area can still be found by breaking it down into smaller, easier to calculate sections.
The area between a graph and the x-axis is useful in real life for calculating quantities such as distance, volume, and speed. For example, if a graph represents the speed of a car over time, the area between the graph and the x-axis would represent the total distance traveled by the car.
Yes, there is a shortcut for finding the area between a graph and the x-axis called the integral. The integral is a mathematical concept that allows for the calculation of the area under a curve, even if the graph is not a straight line. It is a more efficient and accurate method for finding the area between a graph and the x-axis.