Mathematics - Area Under Curves Question with Solution | TestHub

The equation of the curve is $x^2=by$. In the first quadrant, $x=\sqrt{b}\sqrt{y}$.

The area bounded by the curve and the lines $y=1$ and $y=4$ in the first quadrant is given by:

${\int }_1^{4}xdy=28$

${\int }_1^4\sqrt{b}\sqrt{y}dy=28$

$\sqrt{b}{\left[\frac{2}{3}{y}^{3/2}\right]}_1^4=28$

$\frac{2}{3}\sqrt{b}(4^{3/2}-1^{3/2})=28$

$\frac{2}{3}\sqrt{b}(8-1)=28$

$\frac{14}{3}\sqrt{b}=28$

$\sqrt{b}=28\times \frac{3}{14}$

$\sqrt{b}=6$

$b=36$

Answer: $36$