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

1 Answer
Sep 17, 2014

This is an integration problem. We will find the area under the curve #cos(x)# over the interval #[-pi/2,pi/2]#. This is inclusive because of the square brackets.

On the unit circle remember that the positive side of y-axis corresponds to #pi/2# and a coordinate of #(0,1).# The y-coordinate corresponds to #1.#

On the unit circle remember that the negative side of y-axis corresponds to #-pi/2# and a coordinate of #(0,-1).# The y-coordinate corresponds to #-1.#

#int_(-pi/2)^(pi/2)cos(x) dx#

#=[sin(x)]_(-pi/2)^(pi/2)=[sin(pi/2)-sin(-pi/2)]=1-(-1)=2#

Watch this problem solved here