The image shows a shaded region under a curve, and you want to find the area of this region. The relevant curves given in the image are:

1. $y = \frac{4}{x^2}$
2. $y = 0$
3. $x = 1$
4. $x = 5$

To find the area of the shaded region, we need to compute the definite integral of the function $y = \frac{4}{x^2}$ from $x = 1$ to $x = 5$.

The area $A$ is given by:

$A = \int_{1}^{5} \frac{4}{x^2} \, dx$

Let's calculate this integral.The area of the shaded region under the curve $y = \frac{4}{x^2}$ from $x = 1$ to $x = 5$ is $\frac{16}{5}$ or 3.2 square units.

Would you like more details on how this was computed or have any other questions?

Related Questions

1. How do you compute the integral of a different function over a specific interval?
2. What are the properties of the function $y = \frac{4}{x^2}$?
3. How can we approximate the area under a curve using numerical methods?
4. What is the physical interpretation of finding the area under a curve in different contexts?
5. How does changing the limits of integration affect the calculated area?

Tip:

Remember that definite integrals represent the net area between the curve and the x-axis over a specified interval.