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galben [10]
2 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]2 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]2 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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