The area of the region enclosed by the curves \( y = x^2 - 4x + 4 \) and \( y^2 = 16 - 8x \) is:
Show Hint
- \( \frac{4}{3} \)
- \( 8 \)
- \( \frac{8}{3} \)
- \( 5 \)
The Correct Option is C
Solution and Explanation
To find the area enclosed by the curves, we need to set up an integral. First, let's express both curves in terms of \( y \) and solve for the intersection points. The first curve is \( y = x^2 - 4x + 4 \) (a parabola) and the second curve is \( y^2 = 16 - 8x \), which is a sideways parabola.
Next, we solve for the intersection points by equating the two curves, and then integrate the difference of the two functions to find the enclosed area.
After solving the integration, the area enclosed by the curves is \( \frac{8}{3} \).
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