Source: Extra Practice
Calculate the area of the region bounded by the curve y = x³, the x-axis, and the ordinates x = -1 and x = 1.
Options
Option A
0 sq. units
Option B
1/4 sq. unit
Option C is correct
1/2 sq. unit
Option D
1 sq. unit
Explanation
Area must be positive. From x = -1 to 0, x³ is negative, so we take the absolute value. Area = |∫[-1 to 0] x³ dx| + ∫[0 to 1] x³ dx = |[x⁴/4] from -1 to 0| + [x⁴/4] from 0 to 1 = |0 - 1/4| + (1/4 - 0) = 1/4 + 1/4 = 1/2. Option A is the result of a simple definite integral without taking absolute values for area. B and D are calculation errors.