Question

The area between $y^2 + 4x - 8 = 0$, the x-axis and the line $x = 1$ is

• A. $\frac{4}{3}$ sq unit
• B. $\frac{2}{3}$ sq unit
• C. $\frac{1}{3}$ sq unit
• D. $1$ sq unit

Hint:

Area under curve = $\int y\,dx$ for upper half.

Answer 1

The Correct Option is A

Step 1: $y^2 = 8-4x \Rightarrow y = 2\sqrt{2-x}$. Curve meets x-axis at $x=2$.}
Step 2: Area = $\int_1^2 2\sqrt{2-x}dx$. Let $u=2-x$, then $\int_0^1 2\sqrt{u}du = 2\cdot\frac{2}{3} = \frac{4}{3}$.}
Step 3: Final Answer: $\frac{4}{3}$ sq units.}