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 Question from Lauren, a student: This is from a homework question I can't figure out. Let R be the region in the fourth quadrant enclosed by the x-axis and the curve y= x^2 - 2kx, where k > 0. If the area of the region R is 36 then what is the value of k?

Lauren,

First, if the problem was to find the area enclosed by the x-axis and the curve y = x2 - 2x, could you do that? (Draw a sketch, find where the curve crosses the axis, set up the definite integral including the correct bounds, integrate, plug in the bounds, and simplify.) If you can't, review that stuff in your notes or textbook before you continue.

Now try to compute the area for the formula you gave, but when you come to a k just leave it as a k, in all of the above steps. So one or both of the crossing points might depend on k, the thing you integrate depends on k, the bound of integration may depend on k, and the final answer depends on k.

Set that equal to 36 and solve! (You will get two answers, that's why you were told "k > 0")

Good Hunting!
RD

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