Question

When finding the area under a curve using rectangular strips, as the number of strips n → ∞ ______.

Options

• The calculated area becomes zero

• The strips become triangles

• The sum of strip areas equals the exact area under the curve

• The width of strips becomes infinite

Answer 1

When finding the area under a curve using rectangular strips, as the number of strips n → ∞ the sum of strip areas equals the exact area under the curve.

Explanation:

As n → ∞, each strip's width Δx → 0, and the approximation using rectangles becomes exact. This is precisely the definition of a definite integral as a limit of a sum.