Question

The area bounded by the parabola $y^2=4x$ and its latus rectum is ______

• A. $\frac{4}{3}$
• B. $\frac{16}{3}$
• C. $\frac{8}{3}$
• D. $\frac{32}{3}$

Answer 1

The correct option is C $\frac{8}{3}$

latus rectum is the line that passes through focus

so area bounded will be twice the area of the upper half since they are symmetrical

therefore area =$2{\int }_0^1\sqrt{4x}$

that =$4{\int }_0^1\sqrt{x}=4\frac{x^{\frac{3}{2}}}{\frac{3}{2}}{|}_0^1$

=$\frac{8}{3}$