The area (in square units) of the region bounded by the parabola $y^2=4(x-2)$ and the line $y=2x-8$
Step-by-Step Solution
Key Concept: Substitute $X=x-2$: parabola becomes $y^2=4X$, line becomes $y=2(X+2)-8=2X-4$. Find intersections: $(2X-4)^2=4X\Rightarrow4X^2-16X+16=4X\Rightarrow4X^2-20X+16=0\Rightarrow(X-1)(X-4)=0$. Integrate.
After substitution, integrate between $y=-2$ and $y=4$: $A=\int_{-2}^{4}\left(\frac{y^2}{4}-\frac{y}{2}+2-2\right)dy$... from solution PDF: area $=9$.
Correct Answer: 2