MATH105 April 2011
• Q1 (a) • Q1 (b) • Q2 • Q3 • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 • Q7 • Q8 (a) • Q8 (b) • Q8 (c) • Q9 (a) • Q9 (b) • Q9 (c) • Q9 (d) • Q9 (e) • Q9 (f) • Q9 (g) •
Sketch the region in the first quadrant bounded by the curves
and find the area of this region.
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The area between the curves f(x) and g(x) is given by
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To compute the area, we need to know the points of intersection of the curves. For y=4x and xy=1, i.e. point P, this is when x(4x) = 1, i.e. . Equivalently x=1/2, and y=2.
For y=x and xy=1, i.e. point Q, this is (x,y) = (1,1).
Thus, the total area is
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MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Area between two curves