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For t ≥ 0, let (cosht,sinht) be the point sitting on the curve xˆ2−yˆ2 = 1...

For t ≥ 0, let (cosht,sinht) be the point sitting on the curve xˆ2−yˆ2 = 1 in the first quadrant. Let L be the line connecting the origin to this point.

(a) Find the equation of the line L.


(b) Set up an integral A(t) that computes the area of the region in the first quadrant bounded by the line L,the curve xˆ2−yˆ2 =1,and the line y=0.


(c) Simplify A(t) as much as possible. Hint: There should be one term you do not know how to

integrate, so you should leave this as an integral.

(d) Find A′(t), the derivative of A(t) with respect to t. (e) Use part (d) to determine that A(t) = (1/2)t.

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