Find the area bounded by y = ex , x = 0, and y = 6e-x .
a. 3 - 2(21/2 )
b. 4 - 2(31/2 )
c. 1
d. 6 - 2(51/2 )
e. 7 - 2(61/2 )
f. none of these
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ANSWERS: 1
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Either draw a picture or graph it on your calculator. The area is a triangle. The area of any triangle is 1/2bh. The base could be the side against the y-axis. The height would then be the distance perpendicular from the y-axis to the vertex, which is the intersection of y=ex and y=6e-x. That point is roughly (4.38, 11.9). The x-value is all that matters, because it is the distance from the y-axis to that point, which is the height. So the base is roughly 16.3 and the height is roughly 4.38. Multiply and divide by two.
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