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Find the area of the region bounded by the $$x$$ -axis, the hyperbola $$x ^ { 2 } - y ^ { 2 } = 1$$ , and the straight line from the origin to the point $$( \sqrt { 1 + Y ^ { 2 } } , Y )$$ on that hyperbola. (Assume $$Y > 0$$ .) In particular, show that the area is $$t / 2$$ square units if $$Y = \sinh t$$ .
$$\frac { \ln ( Y + \sqrt { 1 + Y ^ { 2 } } ) } { 2 } \text { sq. units }$$