Question

The area bounded by $y = 1 + \dfrac{8}{x^2}$ and the ordinates $x = 2$ and $x = 4$ is

• A. 2 sq unit
• B. 4 sq unit
• C. $\log 2$ sq unit
• D. $\log 4$ sq unit

Hint:

$\displaystyle\int \frac{1}{x^2}\,dx = -\frac{1}{x} + C$. Break compound integrands into simpler terms before integrating.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Compute $\displaystyle\int_2^4 y\,dx$.
Step 2: Detailed Explanation:
$\displaystyle\int_2^4 \!\left(1 + \frac{8}{x^2}\right)dx = \left[x - \frac{8}{x}\right]_2^4 = \left(4-2\right) - \left(\frac{8}{4} - \frac{8}{2}\right) = 2 - (2-4) = 4$ sq units.
Step 3: Final Answer:
Area $= 4$ sq units.