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How do you find the area under one period of y=sinx?

Answer 1

Isabella Ackerman

See explanation.

The period of #sinx# is #2pi#, so integrate #sinx dx# from #a# to #a+2pi#

#int_a^(a+2pi) sinx dx = {: -cosx]_a^(a+2pi)#

# = = -cos(a+2pi) + cosa = 0#

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Answer 2

Christopher Agresta

To find the area under one period of the function ( y = \sin(x) ), you integrate ( \sin(x) ) over one period, which is typically from ( x = 0 ) to ( x = 2\pi ). The integral of ( \sin(x) ) over this interval is ( 2 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.