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galben [10]
3 years ago
8

Identify each expression and value that represents the area under the curve y=x^2+4 on the interval [-3,2]

Mathematics
2 answers:
Alina [70]3 years ago
8 0

The area under a graph is given by the integral of that function, evaluated in the interval of interest:

\displaystyle \int_{-3}^2 x^2+4\;dx = \left[\dfrac{x^3}{3}+4x\right]_{-3}^2 = \left[\dfrac{2^3}{3}+4\cdot 2\right]-\left[\dfrac{(-3)^3}{3}+4\cdot(-3)\right] = \left[\dfrac{8}{3}+8\right]-\left[-9-12\right] = \dfrac{32}{3}+21 = \dfrac{95}{3}

Ostrovityanka [42]3 years ago
6 0

Answer:

(\frac{95}{3})

Step-by-step explanation:

Equation that represents curve is

y = x² + 4

and we have to find the area

under the curve in the interval of [-3, 2] will be

area = \int\limits^2_ {-3} \,x^{2}+4 dx

= [\frac{x^{3} }{3}+4x ]^{2} _{-3}

= \frac{1}{3}[x^{3}]^2_{-3} +4[x]^2_-3

= \frac{1}{3}[(2)^3(-3)^3]+4[(2)-(-3)]

= \frac{1}{3}[8+27]+4[2+3]

= \frac{1}{3}(35)+20

= (\frac{95}{3})

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Step-by-step explanation:

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One die.

How is this gotten? By finding the probability that a one or one dot appears when the 6 dice are rolled at once. Since there are 6 dice in number, and each die has the same 6 faces containing dots, the probability of getting a one is 1/6. In this case, one out of 6 dice is expected to show one dot.

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This would also represent the probability that 2 dots, 3 dots, or any other number of dots appears on all dice in one toss!

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Kudos!

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3 years ago
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I like the substitution method. Which is when you make one equation equal only x or y and plug it into the other equation)

There is also the graphing method. If you graphed it, it might not be quite as accurate (at least on hand, on computer you would be pretty exact)

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3 years ago
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