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g(x)=int_(2)^(x)(10 t+2)dt

g^(')(3)=

$g(x)=\int_{2}^{x}(10 t+2) d t$ $\newline$ $g^{\prime}(3)=$

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Evaluate definite integrals using the power rule

Full solution

Q.

g(x)=\int_{2}^{x}(10 t+2) d t

\newline

g^{\prime}(3)=

Find Derivative of Integral: We need to find the derivative of the integral from $2$ to $x$ of $(10t + 2) \, dt$ , which is $g(x)$ .
Apply Fundamental Theorem of Calculus: By the Fundamental Theorem of Calculus, the derivative of $g(x)$ is the integrand evaluated at $x$ , so $g'(x) = 10x + 2$ .
Evaluate at $x=3$ : Now we evaluate $g'(x)$ at $x=3$ , so $g'(3) = 10(3) + 2$ .
Calculate Result: Calculating $g'(3)$ gives us $30 + 2$ , which equals $32$ .

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