calculated integral bounded by Y axis
By Joseph Russell •
$\begingroup$
suppose we want to find Find the area bounded by the curve $y=\sqrt{2*x-1}$
$Y$ axis and lines $y=1$ and $y=2$
as i remember ,i should express $x$ as a function of $y$ and calculate
$\int(f(y)dy$
so in this case,we have $y^2=2*x-1$ or
$x=(y^2+1)/2=y^2/2+1/2$
so integral from $y=1$ to $y=2$ is $10/6$,because anti derivative of $y^2/2+1/2$ is $y^3/6+y/2$ and put values,is this correct?thanks in advance
$\endgroup$ 31 Answer
$\begingroup$Considering the are and the shape it has, you may find that area as follows easier. An square with area of $1\times 1$ and the rest as $$\int_1^{5/2} (2-y)dx$$
