Find the area bounded by f(x)=sinx and g(x)=cosx from x=pi/4 to x=((5pi)/4.. Make an accurate sketch of the graphs on the axis below?

Find the area bounded by f(x)=sinx and g(x)=cosx from x=pi/4 to x=((5pi)/4). Make an accurate sketch of the graphs on the axis below.
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1 Answer
May 30, 2018

color(blue)[A=int_(pi/4)^(5pi/4)sinx-cosx*dx=2sqrt2]

Explanation:

The Area due to "x-axis" between two curves given by:

color(red)[A=int_a^by_2-y_1*dx

The interval of our integral x in [pi/4,5pi/4]

now let set up the integral:

A=int_(pi/4)^(5pi/4)sinx-cosx*dx=[-cosx-sinx]_(pi/4)^(5pi/4)

[(-sin(5pi/4)-cos(5pi/4))-(-sin(pi/4)-cos(pi/4))]

[2/sqrt2+2/sqrt2]=4/sqrt2=2sqrt2

show the wanted area below(shaded):
y=sinx blue curve
y=cosx green curve
JamesJames