Question

Doing something weird here...

Answer 1

\[\int\limits_{\frac{ \pi }{ 2 }}^{\frac{ 2\pi }{ 3 }}\cos(x)= \sin(x) |{\pi/2, 2\pi/3}=\frac{ \sqrt{3} }{ 2 }-1\]

Answer 2

It might help to graph cos(x) and the boundaries set up for x

see the attached image. The region we're after is the one highlighted in orange/yellow

Answer 3

Notice how that region is BELOW the x axis. So the result of the integral is negative. Your teacher or book is probably wanting the area to be positive. So just place your result in absolute value bars and simplify.

Answer 4

Ah got it, thank you

Answer 5

It's difficult to visualize