Question

Find area bounded by curves $\left\{\right(x,y):y\ge x^{2}andy=\mid x\mid \}$

• A. $\frac{5}{3}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{9}$

Answer 1

Answer: (C)

$\frac{1}{3}$

$y=\mid x\mid$$=\{x;x\ge 0-x;x<0\}$

$P$ and $Q$ are

$x^2=x{x}^2-x=0x(x-1)=0$

$x=0,1$

$Q=1$

similarly

$p=-1$

$A={\int }_0^{1}x-x^{2}dxA={[\frac{x^2}{2}-\frac{x^3}{3}]}_0^{1}A=\frac{1}{2}-\frac{1}{3}A=\frac{1}{3}$