Question

finding exact area between curves

Answer 1

find the exact area between\[f(\theta) = \sin \theta\] and \[g(\theta) = \cos \theta\] for \[0 \le \theta \le 2pi\]

Answer 2

The area is given by:
\[\int\limits_0^{2 pi} \sin(\theta) - \cos(\theta) d \theta\]

Answer 3

is that the complete answer to that since i can't know the exact values of theta? or is that what i need to use to solve it?

Answer 4

\[
\int_0^{\pi/4} (\cos(\theta) -\sin(\theta)) d\theta+\\
\int_{\pi/4}^{5\pi/4} (\sin(\theta) -\cos(\theta)) d\theta+\\
\int_{5\pi/4}^{2\pi} (\cos(\theta) -\sin(\theta)) d\theta\\

\]
We have to divide the interval to have one function above the other in the whole
sub-intervals.

Answer 5

\[\sqrt{2}-1 +\\
2 \sqrt 2+\\
1 + \sqrt 2= 4 \sqrt 2

\]