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Suppose a unit circle, and any arc S on the unit circle in the first quadrant. No matter where S is provided, the area between S and the x-axis plus the covered area between S and y-axis is constant! Moreover, that constant is same to the length of S:
A + B = s2 - s1.
In Figure, note that regions A and B overlap; in that part the area is counted double times. The quantity (s2 - s1) shows the length of S along the arc from s2 to s1.
Before going to solving differential equations we must see one more function. Without Laplace transforms this would be much more hard to solve differential equations which involve
Given f (x) = - x 2 + 6 x -11 determine each of the following. (a) f ( 2) (b) f ( -10) (c) f (t ) Solution (a) f ( 2) = - ( 2) 2 + 6(2) -11 = -3 (
0.25+25
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