Mathematics - Area Under Curves Question with Solution | TestHub

The given curves are $y^2=16x$ and $x=4$.

The area bounded by the parabola and the line is symmetric about the x-axis.

The required area $A$ is given by:

$A=2{\int }_0^{4}ydx$

$A=2{\int }_0^4\sqrt{16x}dx$

$A=8{\int }_0^4{x}^{1/2}dx$

$A=8{\left[\frac{x^{3/2}}{3/2}\right]}_0^4$

$A=\frac{16}{3}\left[4^{3/2}-0\right]$

$A=\frac{16}{3}\times 8=\frac{128}{3}$ sq. units.

Answer: $\frac{128}{3}$ sq. units