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

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Homework Help Overview

The problem involves finding the area between the curves defined by the functions y=2sin(x/3) and y=2x/pi over the interval 0 < x < pi. The original poster has sketched the graphs of these functions and is seeking confirmation of their work.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to confirm their graphical work and calculations related to the area between the curves. Some participants question the clarity of the posted work and suggest entering equations directly into the text box for better readability. Others note the order of the integrands and discuss the points of intersection between the two graphs.

Discussion Status

The discussion is ongoing, with participants providing feedback on the clarity of the original poster's work and addressing potential issues with the calculations. There is an acknowledgment of the intersection points of the graphs and the relative positions of the functions over the specified intervals, but no consensus has been reached regarding the correctness of the area calculation.

Contextual Notes

Participants have noted that the original poster's scanned work was difficult to read, which may affect the clarity of the discussion. There is also a mention of the need for proper formatting in future posts to facilitate understanding.

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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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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.
 
Ive adjusted the contrast and looks okay on my mac - let me know if it is still faint.

Cheers
 
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.
 

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