Find the area of the “triangular” region in the first quadrant bounded on the left by the y-axis and on the right by the curves y = sin x and y = cos x

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#1

Find the area of the “triangular” region in the first quadrant bounded on the left by the y-axis and on the right by the curves y = sin x and y = cos x.

Answer:

First, realize this is an integration problem as we are finding area under a curve.
Then, we need to see what is happening with the graph. Notice the region you are looking for is the area between cos(x) and sin(x). (Cos(x) is above sin(x), which is an important detail).
Now we must find our bounds for our integral. The lower bound will be x=0, as the region is bound by the x-axis. The upper bound will be given by the intersection of the two curves.
sin(x)=cos(x)
tan(x)=1
x=arctan(1)
x=π/4
Now we know our bounds and can compute the integral.
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