https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/ab-8-4/v/evaluating-simple-definite-integral 2021-04-13T17:49:49Z Area between a curve and the x-axis Based on the fundamental theorem of calculus, we can use antiderivatives to compute integrals. Sal Khan video https://cdn.kastatic.org/googleusercontent/zJdRquplJTO_knvg5fI_SdOA8rSlJ7wOoSiGVFlDXu83zaqVQYyBKHqPLgC-SLljMQJYU_vaAtSvzUdSRXO8eSQE Area between a curve and the x-axis Based on the fundamental theorem of calculus, we can use antiderivatives to compute integrals. https://cdn.kastatic.org/ka-youtube-converted/xR4AnXDBnsw.mp4/xR4AnXDBnsw.mp4 354 Second fundamental theorem of integral calculus https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/ab-8-4/v/definite-integrals-and-negative-area 2020-09-27T22:59:01Z Area between a curve and the x-axis: negative area With integrals, it can be helpful to introduce the notion of "negative area".  See why! Sal Khan video https://cdn.kastatic.org/googleusercontent/BI5mO5pUQA6S0GUaCmG_KjTm9tCFztaBOMIDSDC_hSr_a5MTGZaxy_3rcDqncYL6PMagubYHdukzG-wdKH6fHq8E Area between a curve and the x-axis: negative area With integrals, it can be helpful to introduce the notion of "negative area".  See why! https://cdn.kastatic.org/ka-youtube-converted/MM0FTzvedH4.mp4/MM0FTzvedH4.mp4 448 Second fundamental theorem of integral calculus https://www.khanacademy.org/math/class-12-tg/x6469e28db15923ec:definite-integrals/x6469e28db15923ec:the-fundamental-theorem-of-integral-calculus/e/fundamental-theorem-of-calculus 2025-05-05T08:14:25.350149109Z Area using definite integrals Use definite integrals to find the area between a function and the x-axis. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8c/e/evaluating-definite-integrals 2025-03-12T14:20:10.072734823Z Definite integrals: reverse power rule Evaluating definite integrals using the fundamental theorem of calculus Bill Scott exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8c/v/evaluating-definite-integral-with-power-rule 2022-10-07T01:21:57.107451925Z Definite integral of rational function Sal finds the definite integral of (16-x³)/x³ between -1 and -2 using the reverse power rule. video https://cdn.kastatic.org/ka_thumbnails_cache/3bff0686-ef4c-4323-8297-47f9cb499b30_1280_720_base.png Definite integral of rational function Sal finds the definite integral of (16-x³)/x³ between -1 and -2 using the reverse power rule. https://cdn.kastatic.org/ka-youtube-converted/4WJUEXIksH0.mp4/4WJUEXIksH0.mp4 305 Second fundamental theorem of integral calculus https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8c/v/definite-integral-of-cube-root 2022-10-07T01:21:57.107451925Z Definite integral of radical function Sal finds the definite integral of 12∛x between -1 and 8 using the reverse power rule. video https://cdn.kastatic.org/ka_thumbnails_cache/0eb5b97b-619f-48bb-aa65-6cefe42585e4_1280_720_base.png Definite integral of radical function Sal finds the definite integral of 12∛x between -1 and 8 using the reverse power rule. https://cdn.kastatic.org/ka-youtube-converted/5UWdzPq8_Qs.mp4/5UWdzPq8_Qs.mp4 231 Second fundamental theorem of integral calculus https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8c/v/definite-integral-of-sine-based-function 2022-10-07T01:21:57.107451925Z Definite integral of trig function Sal finds the definite integral of 9sin(x) between 11π/2 and 6π. video https://cdn.kastatic.org/ka_thumbnails_cache/d6d8b592-35db-4722-94e3-644231717935_1280_720_base.png Definite integral of trig function Sal finds the definite integral of 9sin(x) between 11π/2 and 6π. https://cdn.kastatic.org/ka-youtube-converted/ldLdWj6DLTw.mp4/ldLdWj6DLTw.mp4 300 Second fundamental theorem of integral calculus https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8c/e/evaluating-definite-integrals-2 2025-05-05T08:14:25.350149109Z Definite integrals: common functions Evaluate definite integrals with a variety of functions including rational, square root, cube root, exponential, and natural logs. Tomer Gal exercise