Calculus find area between 2 curves

Question

Hi guys I was working out this math problem, but didn't get it right.

I first found that the $2$ curves intersect at $x=7$;

I then found the integral of $y = \sqrt{\frac{343}{x}}$ from $x=\frac{343}{289}$ to $x=14$

I subtracted the integral of $y=x$ from $x=7$ to $x=14$

I then got my final answer of $98\sqrt{2} - \frac{3871}{34}$

So, what did I do wrong?

Answer 1

$$\int_{7}^{14} (y-\frac {343}{y^2}) \,dy = \frac {y^2}{2}]_{7}^{14} - \frac {343}{2y^2}]_{7}^{14} = 49$$ Indeed, you have to find the point when two curves meet which is $$y = \frac {343}{y^2}$$ $$y=7$$ So you have to integrate the area between two curves from $y=7$ to $y=14$.