You are asked to draw a triangle using three of the following angles: 0°, 30°, 45°, 55°, 60°, 80°, 90°, 105°. Which triangle can
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The graph of is a horizontal line. So the area under
on [0, 8] is equal to the area of a rectangle with length 8 and height 2, or 16.
The graph of is the upper half of a circle with radius
. It's symmetric about
, so on the interval [0, 8], we're considering a quarter of the circle. The area of such a sector is
.
Then use the fact that the definite integral is distributive over sums, meaning
