Question

The area of the region bounded by the curve \( y = 3x^2 \) and the x-axis, between \( x = -1 \) and \( x = 1 \), is:

• A. 2 sq. units
• B. 4 sq. units
• C. \( \frac{55}{27} \) sq. units
• D. \( \frac{55}{23} \) sq. units
• E. \( \frac{1}{2} \) sq. units

Hint:

For symmetric curves about the x-axis, the area between the curve and the x-axis can be computed by integrating the positive part over the interval.

Answer 1

The Correct Option is A

Step 1: The area under the curve is given by the integral: \[ \int_{-1}^1 3x^2 \, dx. \] Step 2: Integrate the function: \[ \int 3x^2 \, dx = x^3. \] Step 3: Now evaluate the integral: \[ \left[ x^3 \right]_{-1}^1 = 1^3 - (-1)^3 = 1 + 1 = 2. \]