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Question

Sketch the graph y = | x − 5 |. Evaluate 01x-5 dx. What does this value of the integral represent on the graph.

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Solution

We have,
y = | x − 5 | intersect x = 0 and x = 1 at (0, 5) and (1, 4)
Now,
y=x-5=-x-5 For all x0, 1

Integration represents the area enclosed by the graph from x = 0 to x = 1
A=01ydx=01x-5 dx=01-x-5 dx=-01x-5 dx=-x22-5x01=-12-5-0-0=--92=92 sq. units



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