Find the area of the shaded region given two points and the function y=cosx. Here's a figure (page 4 figure 7)
math.upenn.edu/~deturck/m103/rogawski/chap6odd.pdf
I apologize, but as an AI text-based bot, I'm unable to access external websites or view specific figures. However, I can still help you with the process of finding the area of a shaded region between a curve and the x-axis.
To find the area of the shaded region given the function y = cos(x) and two points, you can follow these general steps:
1. Identify the x-coordinates of the two points that define the region.
2. Determine the limits of integration by finding the x-values where the curve intersects the x-axis or the two given points.
3. Set up the definite integral for the area between the curve and the x-axis.
4. Solve the integral to find the area.
If you provide the x-coordinates of the two points or any additional information, I can guide you through the specific steps of finding the area of the shaded region.
To find the area of the shaded region, you can follow these steps:
1. Open the link provided (math.upenn.edu/~deturck/m103/rogawski/chap6odd.pdf) to access the figure.
2. Navigate to page 4 and locate figure 7.
3. Once you have the figure in front of you, identify the two points mentioned.
4. Look at the axes and determine the values of the x-coordinate for the two given points.
5. Use the function y = cos(x) to compute the corresponding y-coordinates for the two points on the graph.
6. Connect the two points with a straight line on the graph to create a triangle, considering the x-axis as the base of the triangle.
7. Determine the length of the base of the triangle by calculating the difference between the x-coordinates of the given points.
8. Calculate the height of the triangle by finding the difference between the corresponding y-coordinates of the given points, which will be the difference between cos(x1) and cos(x2).
9. Use the formula for the area of a triangle, A = (base * height) / 2, to find the area of the shaded region.
10. Evaluate the expression using the values obtained in steps 7 and 8 to determine the area of the shaded region.
By following these steps, you should be able to find the area of the shaded region represented in the given figure.