## Related questions with answers

Question

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

Solution

VerifiedAnswered 9 months ago

Answered 9 months ago

Step 1

1 of 2From the Second Fundamental Theorem of Calculus

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

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

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