Question

The area of region bounded by $x=at,y=2at$ ____ $(0\le t\le 3)$ .

• A. $18a^2$
• B. $104a^2$
• C. $\frac{26a^2}{3}$
• D. $9a^2$

Answer 1

Answer: (D)

$9a^2$

$x=at$ , $y=2at$ , $y=2x$

$A=\int xdy$

$\Rightarrow$ ${\int }_0^3\left(at\right)\left(2at\right)$

$\Rightarrow$ $2a^2{\int }_0^{3}tdt$

$\Rightarrow$ $a^2[t^2{]}_0^3=9a^2$