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Find the exact area bounded by the curves y=sinx and y=cosx in the domain 0≤x≤2pi

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Let,

EQ.1   y = cos x             EQ.2  y = sin x                              

Solve the intersection points between the two equations.

             `y = y`      

       `sin x = cos x`   

Divide both sides by cos x.

       `(sin x)/(cosx) = 1`        

      `tan x = 1`  

Refer to Unit Circle Chart or Table of Trigonometric Function for Special Angle to determine the value of x.

So at the interval `0<=x<=2pi`  values of x are,

     `x = pi/4 and (5pi)/4`      

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