Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. (Round your answer to two decimal places.)
y = 8x^2− 3x, y = x^3−8x+ 2
for some nice graphing, with scalable axes, go to
https://rechneronline.de/function-graphs/
Type in your functions (up to 3 of them). (Type them in, if you copy and paste from the post, the minus sign is really a dash, which the web site does not interpret.)
Set the x range from -3 to 3
Set the y range from -1 to 9
Now you read off the approximate coordinates.
The area is just the integral between those two x-values of the top curve minus the bottom curve.
I got 2812.76 for the answer but it said that's wrong
never mind I figured it out. The correct answer is 498.76
To find the approximate x-coordinates of the points of intersection of the given curves, we can plot the graphs of the two equations and identify their intersection points.
1. Plotting the graphs:
Start by choosing a range of x-values within which you expect the curves to intersect. Let's consider the range -5 to 5 for this example.
a) The first equation is y = 8x^2 - 3x:
Start by calculating the y-values for different x-values within the range. For example, you can take x = -5, -4, -3, ..., 5 and compute the corresponding y-values.
b) The second equation is y = x^3 - 8x + 2:
Similarly, calculate the y-values for the same x-values chosen for the first equation.
2. Identify the intersection points:
Look for points on the graph where the y-values of both equations are approximately equal. These are the points of intersection.
3. Approximate x-coordinates:
Note down the x-values at the points of intersection. Write them down as approximate values since we're using visual estimation on the graph.
4. Find the area bounded by the curves:
The area bounded by the curves can be determined by integrating the difference between the two equations over the interval between the x-coordinates of the intersection points found earlier.
a) Set up the integral:
∫[(top curve) - (bottom curve)] dx
b) Choose appropriate limits of integration:
Choose the x-coordinates of the points of intersection as the limits of integration.
c) Evaluate the integral:
Evaluate the integral using an appropriate method (e.g., antiderivatives, numerical methods).
5. Round the area:
Round your answer to two decimal places as required.
These steps should help you find the approximate x-coordinates of the points of intersection of the given curves and calculate the area bounded by the curves.