Asked by Joana

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!

Answers

Answered by Steve
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.
Answered by Joana
Thank you so much for your time!!
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