Area Under Curves Question 8

Question 8 - 2024 (30 Jan Shift 1)

The area (in square units) of the region bounded by the parabola $\mathrm{y}^{2}=4(\mathrm{x}-2)$ and the line $\mathrm{y}=2 \mathrm{x}-8$

(1) 8

(2) 9

(3) 6

(4) 7

Show Answer

Answer (2)

Solution

Let $X=x-2$

$y^{2}=4 x, \quad y=2(x+2)-8$

$y^{2}=4 x, \ldots y=2 x-4$

$A=\int_{-2}^{4} \frac{y^{2}}{4}-\frac{y+4}{2}$

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