Question

Area enclosed by the curves $y=x^2+1$ and $y=2x+1$, is:

• A. $2/3$
• B. $1$
• C. $4/3$
• D. $8/3$

Answer 1

The correct option is C $4/3$

Intersection points are

$x^2+1=2x+1$

$x^2-2x=0\Rightarrow x(x-2)=0$

$x=0,2$

$y=1,5$

Area$={\int }_0^2(2x+1-x^2-1)dx$

$={\int }_0^2(2x-x^2)dx$

$={(\frac{2x^2}{2}-\frac{x^3}{3})}_0^2$

$=4-\frac{8}{3}=\frac{4}{3}$ sq. units