Any help will be appreciated!

Find the area of the region between x=-3pi/4 and 5pi/4 in the graph enclosed by f(x)=sinx and g(x)=cosx

Thank you!

2 answers

If you want algebraic area, it is zero, since the sinx curve is above cosx just as much as it is below. See

http://www.wolframalpha.com/input/?i=plot+sinx,cosx

The geometric area is just twice the area on the interval [-3π/4,π/4], or

a = 2∫[-3π/4,π/4] cosx-sinx dx = 4√2

Actually, due to symmetry, the area is also just

4∫[-π/4,π/4] cosx-sinx dx

If you try to integrate on the whole interval [-π/4,3π/4] you get zero.
Thank you so much for your time!!
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