# How do you find the area of the region bounded by the curves #y=sin(x)#, #y=e^x#, #x=0#, and #x=pi/2# ?

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To find the area of the region bounded by the curves (y = \sin(x)), (y = e^x), (x = 0), and (x = \frac{\pi}{2}), you need to calculate the definite integral of the difference between the curves (e^x) and (\sin(x)) from (x = 0) to (x = \frac{\pi}{2}).

The integral is given by:

[ \int_{0}^{\frac{\pi}{2}} (e^x - \sin(x)) , dx ]

Evaluate this integral, and you will find the area of the region bounded by the given curves.

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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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