https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-4/v/fundamental-theorem-of-calculus 2020-07-26T09:23:47Z The fundamental theorem of calculus and accumulation functions The fundamental theorem of calculus shows how, in some sense, integration is the opposite of differentiation. Sal Khan video https://cdn.kastatic.org/googleusercontent/5a5w813ehGOYjZSDSvUy07SM9jTFveUepBP1s50I7xFo8KypvecXBj8Y7YPJn3We4MX47FDHbs7CXBAXj83Mf1Vv The fundamental theorem of calculus and accumulation functions The fundamental theorem of calculus shows how, in some sense, integration is the opposite of differentiation. https://cdn.kastatic.org/ka-youtube-converted/C7ducZoLKgw.mp4/C7ducZoLKgw.mp4 483 Fundamental theorem of calculus https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-4/v/applying-the-fundamental-theorem-of-calculus 2022-10-07T01:21:57.107451925Z Finding derivative with fundamental theorem of calculus The Fundamental Theorem of Calculus tells us that the derivative of the definite integral from 𝘢 to 𝘹 of ƒ(𝑡)𝘥𝑡 is ƒ(𝘹), provided that ƒ is continuous. See how this can be used to evaluate the derivative of accumulation functions. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/b73fc1ad-00ec-4b1b-a85b-dc9b4e30b13e_1280_720_base.png Finding derivative with fundamental theorem of calculus The Fundamental Theorem of Calculus tells us that the derivative of the definite integral from 𝘢 to 𝘹 of ƒ(𝑡)𝘥𝑡 is ƒ(𝘹), provided that ƒ is continuous. See how this can be used to evaluate the derivative of accumulation functions. https://cdn.kastatic.org/ka-youtube-converted/WapSrovs7yM.mp4/WapSrovs7yM.mp4 204 Fundamental theorem of calculus https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-4/e/the-fundamental-theorem-of-calculus 2026-04-07T22:59:30.107127435Z Finding derivative with fundamental theorem of calculus Fundamental theorem of calculus practice problems Tomer Gal exercise https://www.khanacademy.org/math/grade-12-math-snc-aligned/x35fdd21198d6755b:integration-i/x35fdd21198d6755b:fundamental-theorem-of-calculus-and-definite-integrals/a/fundamental-theorem-of-calculus-review 2021-04-29T07:49:27Z Fundamental theorem of calculus review Review your knowledge of the fundamental theorem of calculus and use it to solve problems. article https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:integrals-ncert-new/x6f66cbee9a2f805b:untitled-1038/a/understanding-the-fundamental-theorem-of-calculus 2021-04-29T08:01:09Z Warmup: Definite integrals intro Practice evaluating definite integrals by finding the area using shapes (like rectangles & circles) under a function. article https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-6/e/understanding-the-fundamental-theorem-of-calculus 2025-05-05T08:14:25.350149109Z Finding definite integrals using area formulas Practice evaluating definite integrals by finding the area using shapes (like rectangles & circles) under a function. Tomer Gal exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:integrals-ncert-new/x6f66cbee9a2f805b:untitled-1038/v/evaluating-definite-integral-from-graph 2021-06-02T22:36:28Z Worked example: Definite integral by thinking about the function's graph If you already know the area under a curve, you can use it to compute an integral. video https://cdn.kastatic.org/googleusercontent/bOU8uLTtyuHCdiaqSaaTKdGIj5ltQxaovdKGUd-rG5FbuBUk50PFo0PYntOCl0V2bTpryW0DzswxUYYpqJNjR-Lb Worked example: Definite integral by thinking about the function's graph If you already know the area under a curve, you can use it to compute an integral. https://cdn.kastatic.org/ka-youtube-converted/hTTDI49LhjE.mp4/hTTDI49LhjE.mp4 211 Fundamental theorem of calculus https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:integrals-ncert-new/x6f66cbee9a2f805b:untitled-1038/e/evaluating-a-definite-integral-from-a-graph 2026-04-08T01:15:04.085520103Z Definite integrals with area formulas (no graph) Practice evaluating definite integrals from graphs. Tomer Gal exercise