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Ludmilka [50]
3 years ago
6

Please help, no guessing. It would be great if you could explain, too.

Advanced Placement (AP)
2 answers:
navik [9.2K]3 years ago
6 0

a retired dentist, they would have experience and would understand what would be better for patients and all others who are learning. sorry if it wasn't the best, that's all I have. have a wonderful afternoon

Otrada [13]3 years ago
4 0
A retired dentist. Probably to get benefits or something like that.
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I can’t figure this problem out
Natalka [10]

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Alright so the way to do this is to use properties of integrals to make our life easier.

So we have:

\int\limits^4_1 {(3f(x)+2)} \, dx

So lets break this up into two different integrals that represent the same area.

\int\limits^4_0 {f(x)} \, dx - \int\limits^1_0 {f(x)} \, dx = \int\limits^4_1 {f(x)} \, dx

Lets think about what is going on up there. The integral from four to zero gives us the area under the curve of f(x) from four to zero. If we subtract this from the integral from one to zero (the area under f from one to zero) we are left with the area under f from four to one! Hence:

\int\limits^4_1 {f(x)} \, dx

But since we have these values we can say that:

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So we are left with -15 + 6 = -9

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