The area enclosed between the curve y = x^2 + 2 and x-axis between x = 0 and x = 3 is : Option 1: 14 sq. units Option 2: 15 sq. units Option 3: 16 sq. units Option 4: 18 sq. units

Answer: 15 sq. units. Solution: Area = _0^3 (x^2 + 2) dx = [x^3/3 + 2x]_0^3 = 9 + 6 = 15 sq. units.

Calculus

Application of Integrals

Easy

core

The area enclosed between the curve $y = x^2 + 2$ and x-axis between $x = 0$ and $x = 3$ is :

14 sq. units

15 sq. units

16 sq. units

18 sq. units

✅ Correct Option: 2

Area $= \int_0^3 (x^2 + 2)\,dx = \left[\frac{x^3}{3} + 2x\right]_0^3 = 9 + 6 = 15$ sq. units.

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