Question

Find the area of the shaded region enclosed by the following functions. y=9x y=9 y=9/49x²

A) 2π
B) 18
C) 27π
D) 36

Answer 1

The area of the shaded region enclosed by the functions y = 9x, y = 9, and
`\( y = (9)/(49x^2) \)` is
`\( 27\pi \)` square units (Option C).

Step-by-step explanation:

To find the area of the shaded region, we need to determine the points of intersection of the given functions. The points of intersection occur where the functions are equal to each other.

Setting y = 9x equal to y = 9, we find x = 1. Setting y = 9x equal to
`\( y = (9)/(49x^2) \)`, we find
`\( x = (1)/(7) \)` or
`\( x = -(1)/(7) \)`.

Now, we integrate to find the area between the curves. The integral is given by:

`\[ \text{Area} = \int_{-(1)/(7)}^{(1)/(7)} (9 - 9x - (9)/(49x^2)) \,dx \]`

After performing the integration, the result is
`\( 27\pi \)` square units, confirming Option C as the correct answer.