https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/x2dd7feea:applications-of-integration-free-response-questions/a/applications-of-integration-frqs 2026-06-25T15:40:55.094699315Z Applications of integration FRQs What types of questions focus on concepts from this unit? What makes a high-quality response? How are the responses scored? This article walks you through these questions. article https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/x2dd7feea:applications-of-integration-free-response-questions/v/2011-calculus-ab-free-response-1-parts-b-c-d 2026-06-29T20:40:47.259641521Z Using integrals to analyze particle motion: 2011 Calculus AB Free Response #1 (b, c, & d) Integration to find average value of a function. Using a graphing calculator to calculate definite integrals. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/b0d7c915-5407-45e0-9140-6069c62221f0_1280_720_base.png Using integrals to analyze particle motion: 2011 Calculus AB Free Response #1 (b, c, & d) Integration to find average value of a function. Using a graphing calculator to calculate definite integrals. https://cdn.kastatic.org/ka-youtube-converted/OSipkz8vDjE.mp4/OSipkz8vDjE.mp4 484 Free response questions: applications of integration https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/x2dd7feea:applications-of-integration-free-response-questions/v/2011-calculus-ab-free-response-2-c-d 2026-06-29T20:40:47.259641521Z Applying second fundamental theorem of calculus: 2011 Calculus AB free response #2 (c & d) Second fundamental theorem of calculus application Sal Khan video https://cdn.kastatic.org/googleusercontent/iSDXOci63KCnmlpJRf7GxP2e9TNpUmMIO3Or8a217ZieGTSpaEr2zrq1EGukRtP-ggkxsLhfVZ1sUA275P1sx0lL Applying second fundamental theorem of calculus: 2011 Calculus AB free response #2 (c & d) Second fundamental theorem of calculus application https://cdn.kastatic.org/ka-youtube-converted/2axaRJQkfVk.mp4/2axaRJQkfVk.mp4 447 Free response questions: applications of integration https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/x2dd7feea:applications-of-integration-free-response-questions/v/calculating-area-between-curves-ap-calculus-ab-free-response-2011-3b 2026-06-29T20:40:47.259641521Z Calculating area between curves AP Calculus AB free response 2011 3b Calculating the area between curves. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/ae397a16-11a3-4b09-8a81-3c8a9998ec3b_1280_720_base.png Calculating area between curves AP Calculus AB free response 2011 3b Calculating the area between curves. https://cdn.kastatic.org/ka-youtube-converted/0QsFXGAqx9c.mp4/0QsFXGAqx9c.mp4 315 Free response questions: applications of integration https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/x2dd7feea:applications-of-integration-free-response-questions/v/2011-calculus-ab-free-response-3-c 2026-06-29T20:40:47.259641521Z Writing integral for solid of revolution: 2011 Calculus AB free response #3 (c) Disk method to find the volume of a solid generated by rotation of a function Sal Khan video https://cdn.kastatic.org/googleusercontent/NFE-887PfldOnqL4d81Lw45uCerI2EfB0a-bkV_W-PZ0agwokT66ffWhL0hxql5Y4S3Q3BxHHAagYNc9qDRF85s Writing integral for solid of revolution: 2011 Calculus AB free response #3 (c) Disk method to find the volume of a solid generated by rotation of a function https://cdn.kastatic.org/ka-youtube-converted/v-H_7o7EMoU.mp4/v-H_7o7EMoU.mp4 399 Free response questions: applications of integration https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/x2dd7feea:applications-of-integration-free-response-questions/v/2011-calculus-ab-free-response-6c 2026-06-29T20:40:47.259641521Z Finding average value: 2011 Calculus AB free response #6c Average value of a piecewise-defined function on an interval Sal Khan video https://cdn.kastatic.org/googleusercontent/iuJWfGdj6Ecd_Bvny1XS_J5pyrsMQ8Yr0pg9fv1oP9BkYlAN6YdsC9Dt74JaWgZXNGhkUC5vqWktahxcHBUZyH4 Finding average value: 2011 Calculus AB free response #6c Average value of a piecewise-defined function on an interval https://cdn.kastatic.org/ka-youtube-converted/ucghWyc2_qs.mp4/ucghWyc2_qs.mp4 449 Free response questions: applications of integration https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/x2dd7feea:applications-of-integration-free-response-questions/v/2015-ap-calculus-ab-bc-1a 2026-07-05T06:10:45.281152056Z Using accumulation functions 2015 AP Calculus AB BC 1a Using accumulation functions to estimate the amount of water in a pipe. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/a3fa162f-c74c-4409-be6d-b6318a938925_1280_720_base.png Using accumulation functions 2015 AP Calculus AB BC 1a Using accumulation functions to estimate the amount of water in a pipe. https://cdn.kastatic.org/ka-youtube-converted/DQsYrGDDs5I.mp4/DQsYrGDDs5I.mp4 285 Free response questions: applications of integration https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/x2dd7feea:applications-of-integration-free-response-questions/v/2015-ap-calculus-abbc-1d 2026-06-29T20:40:47.259641521Z Writing integral to solve problem in context: 2015 AP Calculus AB/BC 1d When the pipe overflows video https://cdn.kastatic.org/googleusercontent/YmhFgOvD7JF0aUkrhlG_41xGA5WKeCyhM2QPdIMQK-9kZ3fSYbF0B1gZDKhI-H2PLy-RyMTzHNYXmnIqzCb7gfZX Writing integral to solve problem in context: 2015 AP Calculus AB/BC 1d When the pipe overflows https://cdn.kastatic.org/ka-youtube-converted/9Fqy_stBdFk.mp4/9Fqy_stBdFk.mp4 199 Free response questions: applications of integration https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/x2dd7feea:applications-of-integration-free-response-questions/v/2015-ap-calculus-ap-2a 2026-06-29T20:40:47.259641521Z Finding area between curves: 2015 AP Calculus AB 2a Areas between curves video https://cdn.kastatic.org/googleusercontent/SZYUf6Td_I1_ANhJ1apNuOLQRAv8KM4YYMxq-JW0lRzDBtZnZVLNiCayYycTKeIy5BSr6i5qjr2Mqajsr71eZ5Y- Finding area between curves: 2015 AP Calculus AB 2a Areas between curves https://cdn.kastatic.org/ka-youtube-converted/5QY8yvZViO0.mp4/5QY8yvZViO0.mp4 295 Free response questions: applications of integration https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/x2dd7feea:applications-of-integration-free-response-questions/v/2015-ap-calculus-ap-2b 2026-06-29T20:40:47.259641521Z Finding volume of solid with known cross section: 2015 AP Calculus AB 2b Volume of solid with known cross section video https://cdn.kastatic.org/googleusercontent/dXGgG4n-9I55qiT8KLCTeZxvMpENkSbIXWUD1B_x7xdXHVPvFMpOC5guNBogft5JFTgRkw-OX9CvJi92TZ8Mluzl Finding volume of solid with known cross section: 2015 AP Calculus AB 2b Volume of solid with known cross section https://cdn.kastatic.org/ka-youtube-converted/xmVBv7vk3Gg.mp4/xmVBv7vk3Gg.mp4 387 Free response questions: applications of integration https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/x2dd7feea:applications-of-integration-free-response-questions/v/finding-average-velocity-2015-ap-calculus-ab-bc-3d 2026-06-29T20:40:47.259641521Z Finding average velocity 2015 AP Calculus AB BC 3d Finding the average velocity over a given time interval in context. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/9e206071-270a-4f59-9eb1-fd255a7ee9da_1280_720_base.png Finding average velocity 2015 AP Calculus AB BC 3d Finding the average velocity over a given time interval in context. https://cdn.kastatic.org/ka-youtube-converted/31pieUEqLWw.mp4/31pieUEqLWw.mp4 200 Free response questions: applications of integration https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/x2dd7feea:applications-of-integration-free-response-questions/v/2015-ap-calculus-ab-5d 2026-06-29T20:40:47.259641521Z Using function that involves an integral: 2015 AP Calculus AB 5d Constructing expression for f with integral. video https://cdn.kastatic.org/googleusercontent/9O57kGDciw1b2NT5v1OrKINtqryAYpK1oFtTA1n8TpTWqgEvljBHE0RbG1P_5RSpDaaCg8CKXUuc_Zsb4jfF5aI Using function that involves an integral: 2015 AP Calculus AB 5d Constructing expression for f with integral. https://cdn.kastatic.org/ka-youtube-converted/a601bUPEYUs.mp4/a601bUPEYUs.mp4 329 Free response questions: applications of integration