How do you find the area between the two consecutive points of intersection of y=sinx and y=cosx?

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Answer 1 · 2016-08-18T14:57:25

#2sqrt2# areal units

#sinx = cos x at x = pi/4, 5pi/4, ...#

The area in between, within two consecutive points of intersection #x = pi/4 and x= 5pi/4#

#=int (sin x - cos x) d x#, between the limits

#=[-cosx-sinx]#, between the limits

#=[(-sin(5pi/4)-cos(5pi/4)+(sin(pi/4+cos(pi/4)]#

#=[-(-1/sqrt2-1/sqrt2)+(1/sqrt2+1/sqrt2)]#

#=4/sqrt2=2sqrt2#, areal units.-