# How do you find the average value of #sinx# as x varies between #[0,pi]#?

Here, this gives us an average value of

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To find the average value of ( \sin(x) ) as ( x ) varies between ( 0 ) and ( \pi ), you would first integrate ( \sin(x) ) over the given interval, which is ( [0, \pi] ), and then divide the result by the length of the interval. The integral of ( \sin(x) ) with respect to ( x ) is ( -\cos(x) ). Evaluating this integral from ( 0 ) to ( \pi ) gives ( -\cos(\pi) - (-\cos(0)) = -(-1) - (-1) = 1 - (-1) = 2 ). Since the length of the interval ( [0, \pi] ) is ( \pi - 0 = \pi ), the average value of ( \sin(x) ) over this interval is ( \frac{2}{\pi} ).

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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.

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.

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.

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