If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 6

Lesson 2: Approximating areas with Riemann sums
Math
AP®︎/College Calculus AB
Integration and accumulation of change
Approximating areas with Riemann sums
© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

Midpoint & trapezoidal sums

AP.CALC: LIM‑5 (EU), LIM‑5.A (LO), LIM‑5.A.1 (EK), LIM‑5.A.2 (EK), LIM‑5.A.3 (EK), LIM‑5.A.4 (EK)
Google Classroom
You might need: Calculator

Problem

Approximate the area between the x-axis and f, left parenthesis, x, right parenthesis, equals, left parenthesis, x, minus, 3, right parenthesis, squared from x, equals, 0 to x, equals, 6 using a midpoint Riemann sum with 3 equal subdivisions.
The approximate area is
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
Here's a sketch to help you visualize the area:
A shaded region bounded by the graph of the function f of x equals the quantity x minus 3, squared, the x-axis, the equation x equals 0, and the equation x equals 6.
Stuck?
Stuck?