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sergij07 [2.7K]
3 years ago
12

What is the area of the shaded region on the graph shown?

Mathematics
1 answer:
Sindrei [870]3 years ago
5 0

Answer:

As Doris Day said: Good morning to you

Answer 27/2

Step-by-step explanation:

f(x)=-x^3+5x\\F(x)=-\dfrac{x^4}{4} +\dfrac{5x^2}{2} \\F(2)=\dfrac{-16}{4}+\dfrac{20}{2}  =6\\\\F(-1)=\dfrac{-1}{4} +\frac{5}{2} =\dfrac{9}{4} \\g(x)=\dfrac{3x^2}{2}+\dfrac{x}{2}-5\\\\G(x)=\dfrac{x^3}{2}   +x^2-5x\\\\G(2)=4+1-10=-5\\\\G(-1)=\dfrac{-1}{2} +\dfrac{1}{4} +5=\dfrac{19}{4} \\\\\int\limits^2_{-1} {(f(x)-g(x))} \, dx =F(2)-G(2)-(F(-1)-G(-1))\\\\=11+\dfrac{5}{2} =\dfrac{27}{2}

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By using the remainder theorem, determine the remainder when
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Answer:

-123

Step-by-step explanation:

The remainder theorem says that when a polynomial is divided by a linear factor x - c (note the minus sign), the remainder is the value of the polynomial at x = c.

When a polynomial P(x) is divided by x - c, the remainder is P(c).  In other words, to find the remainder, plug in c for x.

You're dividing by x + 4 which is the same thing as x - (-4) -- the role of c is being played by -4.

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3 years ago
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Nata [24]

Hey there! I'm happy to help!

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Step-by-step explanation:

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