Question

The area under the curve y=2√x bounded by the lines x=0 and x=1 is......,Select correct option from the given options.
(a) 4/3
(b) 2/3
(c) 1
(d) 8/3

Answer 1

Area under the curve $y=2\sqrt{x}$ bounded by the ;ines $x=0$ & $x=1$ is given as

$\int y dx=\int_0^12\sqrt{x} dx$

$=2[\frac{x^{3/2}}{3/2}]_0^1$

$=2[\frac{2}{3}]$

$=4/3$

Answer 2

see a rough daigram of area enclosed by x = 0, x = 1 with curve y = 2√x .

area enclosed by curve = $\int\limits^1_0{2\sqrt{x}}\,dx$

= $2\int\limits^1_0{\sqrt{x}}\,dx$

= $2\left[\begin{array}{c}\frac{2}{3}x\sqrt{x}\end{array}\right]^1_0$

= $\frac{4}{3}[1\sqrt{1}-0]$

=$\frac{4}{3}$

hence, option (a) is correct.