Integration as the limit of a sum (Edexcel A-Level Mathematics): Flashcards

An approximation of area under a curve over an interval.

Width is $\Delta x = \frac{b - a}{n}$.

It equals the value of the definite integral.

It's the left endpoint of each subinterval.

To estimate the area under a curve using trapezoids.

Using midpoints of subintervals to find function values.

The function is $f(x) = x^2$ over $[0, 1]$.

It represents the exact area under a curve between points.

The result is $\frac{1}{3}$.

It's foundational for understanding definite integration.