Area Between Curves: Find the Area 0 < x < pi

In summary, the conversation discusses finding the area between two functions on the interval 0 < x < pi. The two functions are y=2sin(x/3) and y = 2x/pi, and the graphs cross at (pi/2, 1). The calculations for the area are provided, with a suggestion to enter equations directly rather than using pictures.
  • #1
zebra1707
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0

Homework Statement



Using the domain 0 < x < pi sketch the two functions y=2sin(x/3) and y = 2x/pi on the same axes. Find the area

Homework Equations





The Attempt at a Solution



I have sketch the graphs. And attached my working so far - can someone confirm my workings so far. Many thanks

Regards
 

Attachments

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  • #2
What you scanned is so faint it's very difficult to read. It would be easier to read if you put your work directly in the text box.
 
  • #3
Ive adjusted the contrast and looks okay on my mac - let me know if it is still faint.

Cheers
 
  • #4
It's clearer now. If you post here often though, you should get into the habit of entering your equations here rather than taking a picture and posting that.

You have your integrands backwards, which is why you're getting negative values (or at least a negative value for the first one.

The two graphs cross at (pi/2, 1). On the interval [0, pi/2] the sine graph is larger than the graph of the line. On the interval [pi/2, pi] the graph of the line is above the graph of the sine function.

Other than that, your antiderivatives appear OK, but I didn't double-check the numbers you got.
 

Related to Area Between Curves: Find the Area 0 < x < pi

1. How do you find the area between two curves?

To find the area between two curves, you need to first graph the two curves and identify the points of intersection. Then, you can use the definite integral to find the area between the two curves. The formula for finding the area between two curves is: A = ∫(f(x) - g(x))dx, where f(x) and g(x) are the two curves and dx is the differential of x.

2. What is the importance of finding the area between two curves?

Finding the area between two curves is important in various fields such as mathematics, physics, and engineering. It can help in calculating volumes, lengths, and other quantities in real-life scenarios. It also helps in understanding the relationship between two functions and their respective areas.

3. Can the area between two curves be negative?

No, the area between two curves cannot be negative. The definite integral only calculates the area under the curve, so it will always be a positive value. If the area between two curves appears to be negative, it means that the curves are intersecting in a way that one curve is above the other at certain points.

4. What happens if the curves do not intersect?

If the curves do not intersect, then there is no area between them. This can happen if the two curves are parallel or if they do not overlap in the given interval. In this case, the area between the two curves will be zero.

5. Can the area between two curves be infinite?

Yes, it is possible for the area between two curves to be infinite. This can happen if one or both of the curves have an infinite discontinuity within the given interval. In this case, the area between the two curves will be undefined or infinite.

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