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Lecture Mathematics 53 - Lecture 4.6 introduce the mean value theorem for integrals and the fundamental theorems of calculus. This chapter presents the following content: Mean value theorem for integrals, the first fundamental theorem of calculus, the second fundamental theorem of calculus. | r I Mean Value Theorem for Integrals The Fundamental Theorems of Calculus Mathematics 53 Institute of Mathematics UP Diliman Instituteof Mathematics UP Diliman MVT FTC Mathematics 53 1 38 For today Mean Value Theorem for Integrals The First Fundamental Theorem of Calculus The Second Fundamental Theorem of Calculus Instituteof Mathematics UP Diliman MVT FTC Mathematics 53 2 38 Recall Definition Let f be defined on a b . The definite integral of f from a to b is i f x dx lim f x Dxi la l A 0 i i if the limit exists and does not depend on the choice of partitions or on the choice of numbers Xị in the subintervals. If the limit exists the function is said to be integrable on a b . Instituteof Mathematics UP Diliman MVT FTC Mathematics 53 3 .
