Introduction
WebAssign is an online education platform that provides digital textbooks, homework, and quizzes for students. It is often used in mathematics courses and offers various tools to help students understand mathematical concepts. One of the tools that WebAssign provides is a plotter that allows students to graph functions and find the area between curves. In this article, we will explore how to use the WebAssign plotter to find the area of the shaded region between curves.
Understanding the Shaded Region
Before we dive into using the WebAssign plotter, we need to understand what the shaded region is. The shaded region refers to the area between two curves on a graph. When two curves intersect, they create a region that is enclosed by both curves. The shaded region refers to the area within this enclosed region.
Using the WebAssign Plotter
To find the area of the shaded region using the WebAssign plotter, we need to follow a series of steps. The first step is to go to the WebAssign website and log in to your account. Once you are logged in, navigate to the appropriate mathematics course and assignment.
Step 1: Graph the Curves
The first step in finding the area of the shaded region is to graph the curves. To do this, click on the “graphing” tab in the assignment window. This will open up the WebAssign plotter.
Step 2: Find the Intersection Points
The next step in finding the area of the shaded region is to find the intersection points of the two curves. These are the points where the two curves intersect and define the boundaries of the shaded region.To find the intersection points, use the “trace” feature in the plotter. Move the cursor along the x-axis until you find a point where the two curves intersect. Once you have found an intersection point, record its x- and y-coordinates.Repeat this process until you have found all the intersection points between the two curves.
Step 3: Determine the Limits of Integration
Once you have found the intersection points between the two curves, you need to determine the limits of integration. These are the values of x that define the boundaries of the shaded region.To find the limits of integration, look at the x-coordinates of the intersection points. The smallest x-coordinate is the lower limit of integration, and the largest x-coordinate is the upper limit of integration.
Step 4: Integrate to Find the Area
The final step in finding the area of the shaded region is to integrate the difference between the two curves over the limits of integration. This will give you the area between the two curves.To integrate the difference between the two curves, subtract one curve from the other and then integrate the result over the limits of integration. For example, if the curves are y = x^2 and y = 2x, the difference is y = x^2 – 2x. Integrate this expression from the lower limit of integration to the upper limit of integration to find the area of the shaded region.
Conclusion
Using the WebAssign plotter, finding the area of the shaded region between curves becomes a lot easier. By following the steps outlined in this article, students can graph functions, find the intersection points, determine the limits of integration, and integrate to find the area. This tool helps students to better understand mathematical concepts and become more proficient in their math courses.