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!
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.
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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