Question

The area above $x$-axis, bounded by the line $x=4$ and the curve $y=f\left(x\right)$ , where $f\left(x\right)=x^2,0\le x\le 1$ and $f\left(x\right)=\sqrt{x},x\ge 1$ is:

• A. 1
• B. 2
• C. 4
• D. 5

Answer 1

The correct option is D 5

$\stackrel{1}{\underset{0}{\int }}{x}^{2}dx+\stackrel{4}{\underset{1}{\int }}\sqrt{x}dx$
$=\frac{x^3}{3}{|{}_0^1+\frac{2}{3}{x}^{3/2}|}_1^4$
$=\frac{1}{3}+\frac{2}{3}(8-1)$
$=\frac{15}{3}=5squnits.$