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Use the Second Fundamental Theorem of Calculus to find F’(x). F(x) = ∫_(-3)^x (t²+3t+2) dt

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From the Second Fundamental Theorem of Calculus

ddx[axf(t)dt]=f(x)\color{#4257b2}\dfrac{d}{dx}\left[\int_{a}^{x} f(t)\,dt \right]=f(x)

F(x)=ddx[3x(t2+3t+2)dt]=x2+3x+2\begin{align*} F'(x)=\dfrac{d}{dx}\left[\int_{-3}^{x} (t^2+3t+2)\,dt \right]&=x^2+3x+2\\\\ \end{align*}

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