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

[zebra1707]

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

 

[Mark44]

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.

 

[zebra1707]

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

Cheers

 

[Mark44]

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.