Question

The area bounded by the parabola $y^2=4x$ and the line $y=2x-4$:

• A. 9 sq. units
• B. 5 sq. units
• C. 4 sq. units
• D. 2 sq. units

Answer 1

Answer: (A)

9 sq. units

$y^2=4x$ and the line $y=2x-4$
area in $QI$+area in QIV
$QI=$ $\stackrel{4}{\underset{0}{\int }}2\sqrt{x}dx-areaof{△}^{le}$
$=$ $\stackrel{4}{\underset{0}{\int }}2\sqrt{x}dx-1/2\left(2\right)\left(4\right)=\frac{32}{3}-4$
$QIV=$ $|\stackrel{1}{\underset{0}{\int }}-\sqrt{x}dx|+1/2\times 1\times 1$
$+\frac{4}{3}+1$
$QI$+QIV$=12-3=9squnits$