Question

Find the area of the shaded region in the graph y=x^2-2

Answer 1

By applying the concept of definite integral and the given restrictions, we conclude that the area of the shaded region in the graph is - 11/12.

How to find the area of the shaded region in the graph y = x² - 2

The area below the curve can be found by using definite integrals, which is defined here in this form:

$I = \int\limits^{1.5}_{0.5} {x^{2}-2} \, dx$     (1)

Now we proceed to calculate the area:

$I = \int\limits^{1.5}_{0.5} {x^{2}} \, dx - 2 \int\limits^{1.5}_{0.5}\, dx$

$I = \frac{x^{3}}{3}|_{0.5}^{1.5} - 2 \cdot x |_{0.5}^{1.5}$

$I = \frac{1.5^{3}-0.5^{3}}{3} - 2 \cdot (1.5 - 0.5)$

$I = -\frac{11}{12}$

By applying the concept of definite integral and the given restrictions, we conclude that the area of the shaded region in the graph is - 11/12.

Remark

The statement is incomplete. Complete form is shown below:

Find the area of the shaded region in the graph y = x² - 2, between x = 0.5 and x = 1.5

To learn more on definite integrals: https://brainly.com/question/14279102

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