# How do you find the area under the graph of #f(x)=cos(x)# on the interval #[-pi/2,pi/2]# ?

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To find the area under the graph of ( f(x) = \cos(x) ) on the interval ([- \frac{\pi}{2}, \frac{\pi}{2}]), you need to integrate ( \cos(x) ) with respect to ( x ) from ( -\frac{\pi}{2} ) to ( \frac{\pi}{2} ). This can be done using the definite integral formula:

[ \text{Area} = \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos(x) , dx ]

Integrating ( \cos(x) ) yields:

[ \int \cos(x) , dx = \sin(x) + C ]

Evaluating the definite integral:

[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos(x) , dx = \sin\left(\frac{\pi}{2}\right) - \sin\left(-\frac{\pi}{2}\right) = 1 - (-1) = 2 ]

So, the area under the graph of ( f(x) = \cos(x) ) on the interval ([- \frac{\pi}{2}, \frac{\pi}{2}]) is (2).

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