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

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SUMMARY

The discussion focuses on finding the area between the curves defined by the functions y=2sin(x/3) and y=2x/pi over the interval 0 < x < pi. Participants confirm that the graphs intersect at the point (pi/2, 1), with y=2sin(x/3) being the upper function from 0 to pi/2 and y=2x/pi being the upper function from pi/2 to pi. The user was advised to enter equations directly into the forum for clarity and to correct the order of integrands to avoid negative area calculations.

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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
 

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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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