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Area Under the Curve

Area Under a Curve

IIT-JEE 1992

Grade 12

Question:

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

(1) $\frac{8}{3}a^2$

(2) $\frac{4}{3}a^2$

(3) $\frac{16}{3}a^2$

(4) $\frac{2}{3}a^2$

Step-by-Step Solution

Key Concept: Express the bounding curve as $y = 2\sqrt{ax}$ and integrate $2y$ with respect to $x$ from $x = 0$ to $x = a$ (the latus rectum).

The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.

Correct Answer: (1)