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Calculate the area under the curve $y=2\sqrt x$ included between the lines $x=0$ and $x=1$.

$\begin{array}{1 1} \frac{4}{3}\;sq.units \\ \frac{2}{3}\;sq.units \\ \frac{1}{3}\;sq.units \\ None\;of\;the\;above \end{array} $

1 Answer

  • The area enclosed by the curve $y=f(x)$,the $x$-axis and the ordinates $x=a$ and $x=b$ is given by $\int_a^b ydx.$
  • $\int x^n dx=\large\frac{x^{n+1}}{n+1}$$+c$.
Step 1:
$y=2\sqrt x$ between $x=0$ and $x=1$.
$\;\;=\int_0^22\sqrt xdx.$
$\;\;=2\int_0^2\sqrt xdx.$
On integrating we get,
$\;\;2\times \large\frac{2}{3}\begin{bmatrix}x^{\Large\frac{3}{2}}\end{bmatrix}_0^1$
Step 2:
On applying limits we get,
Hence the required area is $\large\frac{4}{3}$sq.units.
answered Apr 28, 2013 by sreemathi.v