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Examples 7.1.13(b):

Suppose f(x) = x2 if x 1 and f(x) = 3 if x > 1. Find f(x) dx over the interval [-1, 2].
According to part 2 of the previous result we know that
f(x) dx = f(x) dx + f(x) dx
for a < c < b. Let a = -1, c = 1, and b = 2. Then we have:
f(x) dx = x2 dx = 1/3 (13 - (-1)3) = 2/3
and
f(x) dx = 3 dx = 3 (2 - 1) = 3
Therefore
f(x) dx = 2/3 + 3 = 11/3
Here we computed x2 dx similarly than in a previous example.
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