Area under a curve

Riemann sums as approximations and definite integrals as exact areas.

Standards:AP Calc AB · Unit 6AP Calc AB · Unit 8

Try it: three questions

Real questions from the practice bank. Tap an answer to check it.

Question 1 of 3

Find the area under the curve f(x) = 3x² from x = 0 to x = 2 using integration.

Question 2 of 3

A particle moves along a horizontal line with position function s(t) = t³ − 4t² + 3t meters, where t is time in seconds. Find the acceleration of the particle at t = 2 seconds.

Question 3 of 3

A curve is defined by f(x) = 2x³ − 5x² + 3x. Find f'(2).

How this fits in

Area under a curve is one skill in the Intro to Calculus unit. Students read the unit lesson, then earn a bronze, silver, or gold medal on their last 10 answers. Medals never go down. A mastered unit comes back for review after 1, 3, 7, 16, and 35 days so it stays learned.

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