Any help will be appreciated!

Question

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!

Answer 1

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.

Answer 2

Thank you so much for your time!!