If f(x) = {eq}\int_{1-3x}^3 \frac{\sin(t)}{1 + t^2}dt, {/eq} then f'(x)=


If f(x) = {eq}\int_{1-3x}^3 \frac{\sin(t)}{1 + t^2}dt, {/eq} then f'(x)=

Fundamental Theorem of Calculus

Let's recall the Fundamental Theorem of Calculus, part I. Let f be a continuous function on {eq}[a,b] {/eq} where {eq}x \in [a,b] {/eq} and another function defined as {eq}F(x) = \int_a^x f(t) \;dt {/eq}. Then, its derivative is given by {eq}F'(x) = f(x) {/eq}.

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The Fundamental Theorem of Calculus


Chapter 12 / Lesson 10

Learn about the fundamental theorem of calculus. Identify how to prove the fundamental theorem, and examine graphs and examples of several ways to use it.

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