Jim paddles from one shore of a lake 3 miles wide at 4 mph, and John paddles from the opposite shore at 5 mph. How long will the
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We're given
which immediately tells us that
In other words, swapping the limits of the integral negates its value.
Also,
The integral we want to compute is
which we can do by splitting up the integral at x = 4 and using the known values above. Then the integral we want is