Question

Identify each expression and value that represents the area under the curve y = x2 4 on the interval [-3, 2].

Answer 1

The area under the curve y = x² + 4 on the interval [-3, 2] exists $\frac{95}{3}$.

What is the area under the curve y = x² + 4 on the interval [-3, 2]?

The area under a curve between two points exists seen by accomplishing a definite integral between the two points. To estimate the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. This area can be estimated by utilizing integration with given limits.

The equation that represents the curve exists

y = x² + 4

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

$&\text { area }=\int_{-3}^{2} x^{2}+4 d x$

$&=\left[\frac{x^{3}}{3}+4 x\right]_{-3}^{2}$

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

simplifying the above equation, we get

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

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

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

$&=\left(\frac{95}{3}\right)$

Therefore, the area under the curve y = x² + 4 on the interval [-3, 2] exists $\frac{95}{3}$.

To learn more about area under the curve refer to:

brainly.com/question/2633548

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