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  3. ZuAI AP College Board Calculus AB/BC
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The Fundamental Theorem of Calculus and Accumulation Functions

Benjamin Wright

Benjamin Wright

6 min read

Next Topic - Interpreting the Behavior of Accumulation Functions Involving Area
Study Guide Overview

This study guide covers the Fundamental Theorem of Calculus, which connects differentiation and integration. It explains how to find the derivative of an integral, including examples with accumulation functions where the upper bound is a function of x. Practice problems and solutions are provided to reinforce the concepts.

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Previous Topic - Riemann Sums, Summation Notation, and Definite Integral NotationNext Topic - Interpreting the Behavior of Accumulation Functions Involving Area

Question 1 of 9

If h(x)=∫2x(3t2+1)dth(x) = \int_{2}^{x} (3t^2 + 1) dth(x)=∫2x​(3t2+1)dt, what is h′(x)h'(x)h′(x)?

3x^2 + 1

6x

x3+xx^3 + xx3+x

0