Recall the equation for a circle with center ( h , k ) (h,k) and radius r r. At what point in the first quadrant does the line w
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Recall that a circle of radius 2 centered at the origin has equation
where the positive root gives the top half of the circle in the x-y plane. The definite integral corresponds to the area of the right half of this top half. Since the area of a circle with radius
You have
Another way to verify this is to actually compute the integral. Let
Recall the half-angle identity for cosine:
This means the integral is equivalent to