Question

The area bounded by the line \( y = x \), X-axis and the lines \( x = -1 \) and \( x = 4 \) is equal to .......... (in square units).

• A. \( \frac{2}{17} \)
• B. 8
• C. \( \frac{17}{2} \)
• D. \( \frac{1}{2} \)

Hint:

To find the area under a linear function, integrate the function over the given limits.

Answer 1

The Correct Option is B

Step 1: Set up the integral for the area.
The area under the curve \( y = x \) from \( x = -1 \) to \( x = 4 \) is given by the integral: \[ A = \int_{-1}^{4} x \, dx \]

Step 2: Calculate the integral.
\[ A = \left[ \frac{x^2}{2} \right]_{-1}^{4} = \frac{4^2}{2} - \frac{(-1)^2}{2} = \frac{16}{2} - \frac{1}{2} = 8 - \frac{1}{2} = 8 \]

Step 3: Conclude.
Thus, the area is 8 square units. The correct answer is option (ii).

Final Answer: \[ \boxed{8} \]