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Splitting Integrals at Intersections and Sign Changes
Grade Level
Calculus I
CAL1.139 Splitting Integrals at Intersections and Sign Changes
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For D(x)=f(x)-g(x) = -(x-2)(x-5)(x-8) on 1 <= x <= 9, choose the correct area setup.
A
No interior split; int_{1}
9
[D(x)] dx
B
Split at x = 2, x = 5, and x = 8; int_{1}
2
[D(x)] dx + int_{2}
5
[-D(x)] dx + int_{5}
8
[D(x)] dx + int_{8}
9
[-D(x)] dx
C
Split at x = 2, x = 5, and x = 8; int_{1}
2
[D(x)] dx + int_{2}
5
[D(x)] dx + int_{5}
8
[D(x)] dx + int_{8}
9
[D(x)] dx
D
Split at x = 2 and x = 5; int_{1}
2
[D(x)] dx + int_{2}
5
[-D(x)] dx + int_{5}
9
[D(x)] dx
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