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Question

The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A. Then A4 is equal to

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Solution


A=5π4π4(sinxcosx)dx=[cosxsinx]5π/4π/4=[(cos5π4+sin5π4)(cosπ4+sinπ4)]

=[(1212)(12+12)]
=42=22
A4=(22)4=64

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